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LESSONS IN 



RACTICAL ELECTRICITY 



PRINCIPLES, EXPERIMENTS, AND 
ARITHMETICAL PROBLEMS 



AN ELEMENTARY TEXT-BOOK 

BY 

C. WALTON SWOOPE 

ASSOCIATE MEMBER AMERICAN INSTITUTE OF ELECTRICAL ENGINEERS, 

INSTRUCTOR OF APPLIED ELECTRICITY AT THE 

SPRING GARDEN INSTITUTE, 

PHILADELPHIA 



NEW YORK 

D. VAN NOSTRAND COMPANY 

23 Murray and 27 Warren Streets 

1901 









Copyright, 1901, by C. Walton Swoope. 



PREFACE 

Five years ago the author prepared a private edition of 
''Lessons in Practical Electricity," which was published by 
the Spring Garden Institute for the use of its evening classes 
in practical electricity. 

The demand for the book arose from two facts : First— 
these classes, being composed of young men engaged in 
various occupations who desired to obtain a beginner's knowl- 
edge of the principles and arithmetic of applied electricity, 
were very large ; Second — an unsuccessful attempt was made 
to obtain a book suitable for thoroughly supplementing a 
combined course of lectures and individual laboratory work. 

The educational success attained at the Institute, and also 
at several other schools which secured the privilege of obtain- 
ing copies of the edition (now exhausted), and the fact that 
the former situation had again to be met, seemed to warrant 
the preparation of the present volume, which has been 
entirely re-written and several hundred new illustrations 
introduced. 

In day and evening schools of applied sciences the lecture 
room demonstrations and experiments are supplemented by 
individual laboratory work on the part of the student, this 
being recognized as essential to his best interests. Since the 
work of instruction is thus divided between the lecture hall 
and the laboratory, an attempt has been made to combine 
in this book : (1) the principles of electricity upon which 
the practical applications of to-day depend ; (2) the experi- 
mental demonstration of these principles ; (3) the elements 
of the arithmetic of electricity used in making practical elec- 
trical measurements and calculations. 



IV PREFACE 

Illustrations have been generously introduced to make the 
principles clear, in preference to pictures of electrical machin- 
ery in common use, these being supplemented by numbered 
experiments, which may be conducted with simple and inex- 
pensive, yet efficient, apparatus such as that described, which 
was designed for, and is now used by the Institute. 

A knowledge of fractions, decimals and simple proportion 
will enable the student to make nearly all the calculations, 
but if deficient in these subjects, he is advised to study the 
same in connection with this part of the book. 

The numbered formulae used throughout the text are 
simple expressions for the accompanying rules ; the deriva- 
tion of each being explained and illustrated b}^ a practical 
problem completely solved, with each step indicated by the 
proper formula. 

Questions at the end of each lesson are introduced as a 
special home work feature, and numerical unsolved prob- 
lems, with answers, are also given at the end of many of the 
lessons for the same purpose. 

A number of reference tables of useful information and 
experimental data have been inserted, and two large instruc- 
tion plates inclosed in the cover pocket. 

In the Appendix will be found a summary and index of 
the formulae explained and used in the book, also some 
mensuration formulae. 

Permission for the reproduction of some cuts from Pro- 
fessor Jamiesoirs " Elementary Electricity " has been kindly 
granted by the publishers. 

Prepared from necessity, rather than from any desire to 
increase the copious number of books on the subject, it is 
hoped that this volume will achieve the desired object and 
assist other collaborators in the same field. 

Philadelphia, September, 1901. 



CONTENTS. 



LESSON I. 

MAGNETISM. 



PAGE 

Natural Magnets — Artificial Magnets— Definition of a Magnet — 
The Poles — Magnetic Attraction and Repulsion — Two Kinds 
of Magnetic Force — The Two Poles Inseparable — Magnetic 
Substances — Magnetisable Metals— Classification of Mag- 
nets—Questions, 1 

LESSON II. 

MAGNETISATION. 

To Make an Artificial Magnet — Magnetising Each Half Sepa- 
rately — Magnetisation by Divided Stroke— Magnetisation by 
an Electric Current — Magnetisation by an Electromagnet — 
Making Permanent Steel Magnets— Compound or Laminated 
Magnets — Horseshoe Magnets— Horizontal Magnetic Needle 
— Questions, 6 

LESSON III. 

MAGNETIC FIELDS. 

Magnetic Force — Magnetic Lines of Force — The Magnetic Field- 
Making Magnetic Fields — Axis and Equator of Bar Magnet — 
Questions, 14 

LESSON IV. 

THEORY OF MAGNETISM. 

The Nature of Magnetism — Experimental Proof of the Molecu- 
lar Theory of Magnetism —Breaking a Magnet — Magnetic Sat- 
uration — The Magnetic Difference Between Iron and Steel — 
Retentivity and Residual Magnetism— Destruction of Mag- 
netism by Heat — Strength of a Magnet— Lifting Power of a 

Magnet — Questions, 22 

V 



vi CONTENTS. 

LESSON V. 

MAGNETIC INDUCTION. 

PAGE 

Magnetic Induction Experiments — Magnetic Induction— Action 
and Reaction Equal and Opposite— Magnetic Inductive Effect 
of Like and Unlike Poles — Reversed Polarity — Consequent 
Poles — Magnetic Screens -Questions, 28 

LESSON VI. 

MAGNETIC CIRCUITS. 

Magnetic Circuits — Magnetic Bodies Free to Move — Test for the 
Distribution of Magnetism— Testing Distribution by a 
Needle's Oscillation — Pole Pieces, Armatures, and Keepers- 
Questions, 36 

LESSON VII. 

earth's magnetism. 

The Earth's Magnetism— Polarity of the Earth— The Earth's 
Magnetic Field and Equator— Graphical Field of the Earth's 
Magnetism — The Magnetic Meridian — Declination — Inclina- 
nation or Magnetic Dip — Magnetic Maps or Charts — The 
Mariner's Compass — Magnetisation by the Inductive Effect 
of the Earth's Field— The Earth's Field Directive, Not 
Translative — Neutralizing the Earth's Attractive Force for 
a Needle — Astatic Needles— Questions, . 41 

LESSON VIII. 

VOLTAIC ELECTRICITY. 

Electricity— Electrical Effects— Generation of Electric Currents 
by Chemical Means — A Current of Electricity— Simple Vol- 
taic Cell — Volta's Pile — The Circuit — Conductors and Insu- 
lators — Direction of the Current — Poles or Electrodes and 
Plates — Detector Galvanometer — Potential and Electromo- 
tive Force — Chemical Action in a Voltaic Cell — Why the 
Hydrogen Appears at the Copper Plate— Polarization— Table 
II. Polarization Test — On What the Electromotive Force of 
a Cell Depends— Table III. The Electro-Chemical Series- 
Local Action — Amalgamation— Questions, 49 

LESSON IX. 

BATTERIES 

Primary Batteries— Open Circuit Cells— Closed Circuit Cells- 
Remedies for Polarization— The E. M. F. of Cells— Smee 
Cell— Bichromate Cell— Fuller Bichromate Cell— Partz Acid 



CONTENTS. vii 

PAGE 

Gravity Cell— Bunsen and Grove Cells — Daniell Cell— 
Leclanche Cell — Gonda Leclanche Cell — Carbon Cylinder 
Cell — Edison-Lalande Cell— Chloride of Silver Cell — Dry 
Cells — Classification of Cells — Chemicals for Cells and Some 
Chemical Symbols— Questions, 63 

LESSON X. 

ELECTROLYSIS. 

Effects of the Current — Heating Effect — Magnetic Effect — Chemi- 
cal Effect— Electrolysis — Electrolysis of Copper Sulphate- 
Electrolysis of Zinc Sulphate — Electrolysis of Lead Acetate — 
Electroplating — Electrotyping — Polarity Indicator — Second- 
ary Batteries, Storage Batteries or Accumulators — Direction 
of Current in an Accumulator on Charge and Discharge — 
Commercial Storage Batteries — Questions, 77 

LESSON XL 

MEASUREMENT OF CURRENT STRENGTH. 

Strength of Current— Variation of Current and Current's Effects 
— How the Effects Vary with the Current Strength— Varia- 
tion of Effects with the Same Current Strength Through Dis- 
similar Apparatus — Measurement of Current Strength — Defi- 
nition of the Unit of Current Strength — Definition of a Unit 
Quantity of Current Strength— The Ampere-Hour — Weight 
Voltameters — Voltameter Calculations — Construction of the 
Gas Voltameter — Current Strength Used in Electroplating 
and in Commercial Apparatus— Questions and Problems, . . 87 

LESSON XII. 

RESISTANCE. 

Resistance — Table V. Conductors and Insulators — The Unit of 
Resistance— Laws of Resistance —Table VI. Resistance of a 
Mil- Foot of the Metals— Calculation of Resistance — Wire 
Measure— The Circular Mil— The Square Mil— The Wire 
Gauge — Table of Conductivity and Resistivity of Metals — In- 
ternal Resistance of a Battery— Questions and Problems, . . 103 

LESSON XIII. 
ohm's law and battery connections. 

Electromotive Force (Pressure)— Table IX. Electromotive 
Forces of Batteries and Dynamos— Ohm's Law — Ohm's Law 
Applied to a Battery Circuit— Methods of Varying Current 
Strength— The Size of a Cell— Cells Connected in Series to 
Increase the E. M. F.— Cells Connected in Parallel or Multi- 



viii CONTENTS. 

PAGE 

pie for Quantity — The Internal Resistance of Cells in Series — 
Current from Cells in Series — The Internal Resistance of 
Cells in Parallel or Multiple— Current from Cells in Parallel 
or Multiple— Advantage of Parallel Connection — Advantage 
of Series Connection — Cells grouped in Multiple Series — In- 
ternal Resistance of Any Combination of Cells — Current 
Strength from Any Combination of Cells — Cells Connected 
in Opposition— Questions and Problems, 118 

LESSON XIV. 

CIRCUITS AND THEIR RESISTANCE. 

Conductance of a Circuit— Resistances in Series — Equal Resist- 
ances in Parallel (Joint Resistance) — Unequal Resistances in 
Parallel — Conductivity Method for Conductors in Parallel- 
Resistances Joined in Multiple-Series — Division of Current 
in a Divided Circuit — Potential Difference in Multiple Cir- 
cuits—Current in Branches of Multiple Circuits— Shunts — 
Rheostats — Resistance of Connections — Laboratory Rheo- 
stats — Table X. Resistance of Commercial Apparatus — 
Questions and Problems, 140 

LESSON XV. 

ELECTRO-MAGNETISM. 

Electromagnetism— Direction of the Lines of Force of a Straight 
Current-Carrying Wire — Deflection of a Horizontal Magnetic 
Needle— Right-Hand Rule for Direction of Whirls— Right- 
Hand Rule for Direction of Current or Deflection of Needle 
— Magnetic Field of a Circular Wire Carrying a Current — 
Magnetic Field of a Circular Current — The Helix and Sole- 
noid — Testing the Polarity of a Solenoid — Rules for Deter- 
mining the Polarity of a Solenoid — Graphical Field of a Sole- 
noid—Questions, 153 

LESSON XVI. 

GALVANOMETERS. 

Principle of the Galvanometer— Detector Galvanometer — The 
Use of Long and Short Coil Galvanometers— Classification of 
Galvanometers — Relative Calibration of a Tangent Galva- 
nometer — The Tangent of an Angle— Student's Combination 
Tangent Galvanometer— Directions for Setting up Student's 
Combination Galvanometer — Variation of Needle's Deflection 
With the Turns and Diameter of Coil — Use of the Tangent 
Galvanometer as an Ammeter — Thomson Mirror Reflecting 
Galvanometer — Astatic, Differential and Ballistic Galvanome- 
ters — Table XI. Natural Sines and Tangents— Table XII. 
Tangent Galvanometer Constants — Questions, 167 



CONTENTS. ix 

LESSON XVII. 

ELECTROMAGNETS. 

PAGE 

Magnetisation of Iron and Steel by an Electric Current— Mag- 
netic Field of an Electromagnet— Attractive Force of a Sole- 
noid for an Iron Core — Magnetic Circuits— Typical Forms of 
Electromagnets, Their Construction and Use — Magnetising 
Force, Ampere-Turns — Reluctance — Coarse and Fine Wire 
Electromagnets — Testing the Attractive Force of an Electro- 
magnet—Table XIII. Tractive Force and Magnetic Induction 
— Questions, 184 

LESSON XVIII. 

AMMETERS 

Measurement of Current Strength, Ampere-Meters — Gravity 
Ammeter — Connecting Ammeters in Circuit — Balance Beam 
Ammeter — Thomson Inclined Coil Ammeter — Weston Am- 
meter — Weston Ammeter Shunt — Questions, 200 



LESSON XIX. 

ELECTRICAL WORK AND POWER. 

Force— Different Kinds of Force — Mass and Weight — Work — 
Power — Horse Power of a Steam Engine— Difference Between 
Energy, Force, Work, and Power — Electrical Work — Electri- 
cal Power— Heat and Work — Equivalents of Mechanical and 
Electrical Work — Electrical Horse Power — The Kilowatt — 
The Watt-Hour and Kilowatt-Hour — Electrical Power Cal- 
culations—Electrical Power Formulae— Power from Cells — 
Efficiency of a Battery — Questions and Problems, 209 



LESSON XX. 

MEASUREMENT OF PRESSURE. 

Electromotive Force and Potential Difference — Hydraulic Anal- 
ogy to Illustrate "Volts Lost" — Volts Lost in an Electric 
Circuit— Variation of P. D. in a Circuit — Variation of Po- 
tential Difference with Variation of External Resistance — 
Table XIV. Variation of Current, Pressure, and Resistance 
— Measurement of E. M. F. and P. D. — Construction of 
Voltmeters — Weston Voltmeter— Connecting Voltmeters — 
Measuring High Voltages with Low Range Instrument — 
Volts Lost in Wiring Leads— Comparison of E. M. F. of Cells 
by the Potentiometer. — Questions and Problems, 228 



x CONTENTS. 

LESSON XXL 

MEASUREMENT OF RESISTANCE. 

PAGE 

Measurement of Resistance (Fall of Potential Method)— Measur- 
ing the Resistance of Arc and Incandescent Lamps while 
Burning— Measurement of Resistance (Substitution Method) 
— Drop Method of Comparison— Voltmeter Method — By 
Weston Instruments — Measurement of Resistance-Wheat- 
stone Bridge (Principle of Slide Wire Pattern)— Lamp Chart 
Analogy of Wheatstone Bridge— Construction and Use of 
Slide Wire Bridge— Student's Wheatstone Bridge (Lozenge 
Pattern)— Operating the Bridge — To Measure a Higher Re- 
sistance Than That in the Rheostat— To Measure a Low Re- 
sistance — The Best Selection of Resistances for the Bridge 
Arms— Commercial Wheatstone Bridge — Direct Reading 
Ohmmeter— Questions and Problems, 247 

LESSON XXII. 

ELECTRICAL DEVELOPMENT OF HEAT. 

Heating of Conductors and Their Safe Carrying Capacity — Table 
XV. Current-Carrying Capacity of Copper Wires — Electri- 
cal Development of Heat— Electrical Equivalent of Heat — 
Joule's Law — Relation Between Heat, Mechanical and Elec- 
trical Energy — Relation of Fahrenheit and Centigrade Ther- 
mometer Scales — Relation of Resistance to Temperature — 
Table XVI. Temperature Coefficients — Fuses and Cut-Outs 
—Table XVII. Gauges of Different Wires Fused by 100 
Amperes — Electric Cautery, Blasting, Welding, and Cooking 
— Questions and Problems, 265 

LESSON XXIII. 

ELECTRODYNAMICS. 

Reaction of a Current-Carrying Wire on a Magnet — Automatic 
Twisting of a Current-Carrying Wire Around a Magnetic 
Pole — Rotation of a Current-Carrying Wire Around a Mag- 
netic Pole — Electrodynamics— The Magnetic Fields of Par- 
allel Currents — Laws of Parallel and Angular Currents — 
Currents in Angular Conductors — The Electro-dynamometer 
Portable Dynamometer Ammeter— Dynamometer Wattmeter 
Thomson Recording Wattmeter— Questions, < . 276 

LESSON XXIV. 

ELECTROMAGNETIC INDUCTION. 

Electromagnetic Induction — Currents Induced by a Magnet in a 
Wire— To Find the Direction of the Induced Current (Flem- 
ing's Right-Hand Rule)— Upon what Factors the Induced 



CONTENTS. xi 

PAGE 

E. M. F. Depends— Currents Induced in a Coil by Motion of 
a Magnet — Primary and Secondary Coils — Lenz's Law of In- 
duced Currents — Classification of Induced Currents — Cur- 
rents Induced by Electromagnetism — Five Methods of Pro- 
ducing Induced Currents — Table XVIII. Induction Currents 
— Variation of Induced E. M. F., with the Eate of Change 
of Magnetic Lines of Force (Faraday's Law) — Eddy Currents 
-(Arago's Rotation) — Mutual Induction — Self-Induction — 
Gas Lighting Spark Coil — Inductance— Reactance and Im- 
pedance — Choke Coils— Neutralizing the Effects of Self-in- 
duction — Questions, 293 

LESSON XXV. 

THE INDUCTION COIL. 

Principle of the Induction Coil or Transformer — The Induction 
Coil — The Action of the Coil — Action of the Condenser — 
Construction of Induction Coils — Wehnelt Electrolytic In- 
terrupter — Spark Coil Data — Vacuum Tubes — Roentgen 
Rays (X-Rays) — The Fluorescing Screen and Fluoroscope — 
The Telephone — The Microphone Principle — The Blake 
Microphone Transmitter — The Telegraph— The Signal Sys- 
tem and Circuits— Electric Waves — Wireless Telegraphy — 
Questions, 315 

LESSON XXVI. 

DYNAMO-ELECTRIC MACHINES. 

The Dynamo — Classification of Dynamos — A Simple Dynamo — 
Alternating Current Dynamo — Graphic Representation of an 
Alternating Current — Magneto Alternator — Simple Direct 
Current Dynamo — Graphic Representation of a Direct Cur- 
rent — Multi-Coil Armatures — Gramme Ring Armatures — 
Induced E. M. F. in a Ring Armature — Siemens Drum Arma- 
ture — Advantages of Drum and Ring Armatures — Drum- 
Wound Ring Armatures— Open Coil Armatures — Questions, 334 

LESSON XXVII. 

ARMATURES. 

Armature Core Construction — Eddy Current Loss— The Commu- 
tator and Brushes — Armature Core Insulation — Armature 
Winding — Armature Core Loss-Hysteresis — Armature Re- 
actions — The Act of Commutation of an Armature Coil — 
Sparking at the Brashes— Position of the Brushes — Causes 
of Sparking — Capacity of a Dynamo — Commercial Rating of 
Dynamos — Losses in a Dynamo — Efficiency of a Dynamo — 
Questions, 355 



xii CONTENTS. 

LESSON XXVIII. 

DIRECT CURRENT DYNAMOS. 

PAGE 

Bipolar Field Magnets— Multipolar Field Magnets— Multipolar 
Field Armature Circuits — Constant Current and Constant 
Potential Dynamos — Classification of Dynamos According to 
Their Field Excitation — The Self-Exciting Principle of 
Direct Current Dynamos — The Shunt Dynamo (Constant 
Potential, D. C. ) — Action of the Shunt Dynamo — Action of 
the Series Dynamo (Constant Current)— Compound Ma- 
chines (Constant Potential)— Compound Dynamos in Parallel 
— The Equalizer — Questions and Problems, 372 

LESSON XXIX. 

DIRECT CURRENT MOTORS. 

Comparison Between a Dynamo and Motor— Principles of the 
Motor — Direction of Rotation of Series and Shunt Motors — 
Position of the Brushes on a Motor — Counter Electromotive 
Force of a Motor — Normal Speed of a Motor — Mechanical 
Work Performed by a Motor-Torque — Output and Rating of 
Motors— Motor Speed and Torque— Methods of Motor Speed 
Regulation — Speed Regulation of Series Motors — Series 
Motors for Railway Work — Operating Motors — Efficiency of 
a Motor — Electric Traction— Questions and Problems, . . . 393 

LESSON XXX. 

ELECTRIC LIGHTING. ' 

The Electric Arc — Crater of the Arc — Types of Arcs— Rating of 
Arc Lamps— Arc Lamp Carbons — Arc Lamp Regulation — 
Inclosed Arcs — Alternating Current Arcs — Arc Lamp Circuits 
— Incandescent Lamps— The Lamp Filament — Commercial 
Rating of Incandescent Lamps — Life and Efficiency of a Lamp 
— Incandescent Lamp Circuits — Potential Distribution in 
Multiple Lamp Circuits— Loss on Transmission Lines— In- 
candescent Wiring Calculations— The Three-Wire System — 
Motor Wiring Calculations — Questions and Problems, , . . 415 



CONTENTS. 



Xlll 



LIST OF TABLES. 

Table page 

I. Oscillation Test, 38 

II. Polarization Test, 59 

III. Electro-Chemical Series, 60 

IV. Value of Current Strengths Used in Practice, .... 101 

V. Conductors and Insulators, 105 

VI. Resistance of a Mil-Foot of the Metals, 110 

VII. B. & S. Wire Gauge, 113 

VIII. Comparative Conductivity and Resistance of Metals, . 115 

IX. E. M. F. of Batteries, 118 

X. Resistances of Commercial Apparatus, 150 

XI. Natural Sines and Tangents, 173 

XII. Tangent Galvanometer Constants, 176 

XIII. Tractive Force and Magnetic Induction, 198 

XIV. Variation of Current Pressure and Resistance, .... 235 

XV. Current Carrying Capacity of Copper Wires, ..... 266 

XVI. Temperature Coefficients, 272 

XVII. Gauges of Different Wires Fused by 100 Amperes, . . 273 

XVIII. Induction Currents, 303 

XIX. Sparking Distances in Air, 321 

XX. Spark Coil Dimensions, 323 

XXI. Insulation Test, 359 

XXII. Motor Test, 401 

XXIII. Definition of Practical Electrical Units, 445 

XXIV. Equivalents of Units of Length, 446 

XXV. Equivalents of Units of Area, 447 

XXVI. Equivalents of Units of Volume, 447 

XXVII. Equivalents of Units of Weight, 448 

XXVIII. Equivalents of Units of Energy and Work, 449 

XXIX. Comparative Table of Gauges, 450 

XXX. Decimal Equivalents, . . . 451 

XXXI. Volts Loss on Copper Wire, 451 

XXXII. Useful Equivalents of Electrical Heating, 452 



APPENDIX. 

PAGE 

Summary of Formulae, 436 

Mensuration Formula?, 443 

Tables XXIII to XXXII, 445 

Instruction Plates (2), Cover pocket. 



LESSONS IN PRACTICAL ELECTRICITY. 



LESSON I. 




Fig. 1. — Natural Magnet At- 
tracting Iron Filings. 



MAGNETISM. 

Natural Magnets — Artificial Magnets — Definition of a Magnet — The 
Poles — Magnetic Attraction and Eepulsion — Two Kinds of Mag- 
netic Force — The two Poles Inseparable — Magnetic Substances — 
Magnetisable Metals — Classification of Magnets— Questions. 

1. Natural Magnets. — The name magnet was first applied 
by the ancients to brown-colored stones, known as magnetic 
oxide of iron (Fe 3 OJ because these, as taken from the earth, 
possessed the peculiar property of 
attracting small pieces of iron or 
steel. Later the Chinese discovered 
that if a piece of the ore were freely 
suspended by a string it possessed 
the important property of pointing 
always in a particular direction, 
nearly north and south ; hence they 
gave it the name of lodestone (mean- 
ing leading stone), and used it in this manner to navi- 
gate their ships. Excellent iron is made from magnetic 
oxide of iron which is found in the United States (Arkansas) 
and various other parts of the world. In studying the mag- 
netic attractive force of a piece of lodestone by means of iron 

filings, it will be found 
Mm,.., vufii&MkimitT,. that the attraction for the 

filings seems to be cen- 
tered at two or more 
points on the stone, 
while at other points no 
filings are attracted. 
2. Artificial Mag- 
nets. — The natural magnet possesses yet a third important 
property, namely, that of imparting all of its properties to 

1 




Fig. 



2. — Magnetised Steel Bar Attracting 
Iron Filings. 



PRACTICAL ELECTRICITY. 



Copper 



Thread 



Wire 



a piece of hard iron or steel when they are rubbed together 
without apparently losing any of its original force. This 
steel (a piece of clock spring or a knitting needle will 
answer) will now attract filings, when freely suspended come 
to rest in a northerly and southerly direction, and can be 
used to magnetise another piece of steel. 

Strong artificial magnets are not made from the lodestone, 
as its magnetic force is not strong, but by better methods to 
be mentioned later. Figs. 1 and 2 illustrate a natural and 
artificial steel magnet attracting filings. 

3. Definition of a Magnet. — Given two pieces of similar 
steel, one of which is a magnet and the other not magnetised, 
how would you determine the magnet ? Plunge each piece 
of steel into iron filings ; only the magnetised bar will attract 

them. Suspend each specimen 
separately in a stirrup fastened 
to the end of an untwisted 
thread, the magnet will come 
to rest pointing nearly north 
and south. When turned from 
this position it again assumes 
it, while the piece of unmag- 
netised steel, when so suspend- 
ed, will rest indifferently in 
any position. As a third test, 
the magnetised piece of steel 
can impart its power to another piece of steel. From these 
tests then we can define a magnet as a piece of steel, or other 
magnetised substance, which possesses the properties of attracting 
other pieces of steel or iron, or magnetisable bodies to it, and of 
pointing, when freely suspended in a horizontal position, toward 
the north pole of the earth. 

4. The Poles. — The ends of a magnet are termed its poles. 
The end which points toward the north geographical pole is 
generally called the North pole, and is usually marked on 
that end of the magnet by an N, or a line cut in the steel, 
while the other unmarked end is the South (S) pole. 

By the term polarity we mean the nature of the magnetism 
at a particular point ; that is, whether it is N or S-seeking 
magnetism. 

5. Magnetic Attraction and Repulsion. — Suspend a 
bar magnet in a stirrup, as in Fig. 3, ascertain and mark its 




Steel 



Bar 



Fig. 3. — Testing a Magnet. 



MAGNETISM. 



N-pole and then bring near it the N -seeking pole of another 
bar magnet held in your hand. The N-end of the suspended 
gnet is repelled by the N-end of the magnet in your hand, 



ma 





Fig. 4. — N-Pole Repels N-pole. 

while the S-end of the suspended mag- 
net is attracted by this same N-end. 
In a similar manner it will be found 
that the two S-poles, repel each other, 
while either S-pole attracts the unlike, 
or N-pole. Repeat the above experiments with two 
pieces of magnetite, first ascertaining their N and S-seeking 
points. The N -seeking pole of one piece repels a like, or 
N-pole, of the other piece, but attracts a S-pole ; thus, 
Like poles repel each other but unlike poles attract each other. 

The same experiment can be made with a piece of mag- 
netite and a bar magnet. If the poles of two bar magnets, 
one held in each hand, be plunged into iron filings and then 
the N-poles approached to each other, the magnetic force of 
repulsion will be clearly noted by the repellent action of the 



Fig. 5— S-Pole Attracts N-Pole. 

filings on the two magnets. If unlike 
poles are thus approached, the attractive 
force is shown by the filings bridging the 
air gap between the poles. 

6. Two Kinds of Magnetic Force.— 
The above experiments would indicate two kinds of magnet- 
ism, or two kinds of magnetic poles, which attract or repel 
each other, one pole tending to move toward the geograph- 




4 PRACTICAL ELECTRICITY. 

ical N-pole, and the other pole, toward the geographical 
S-pole. Since we have called the N-pointing, or marked 
pole, the N-pole, and have shown that like poles repel each 
other, then the magnetism of the earth near the N -geographi- 
cal pole must be of the opposite kind, or S-magnetism, since 
unlike poles attract each other. The true N -magnetic pole 
of the earth's magnetism is considered in ^[ 48. 

7. The Two Poles Inseparable.— If a piece of steel be 
rubbed with only one pole of a magnet it will have a N and 
S-pole. Upon breaking it into two equal pieces each piece 
will have a N and S-pole. It is impossible to produce a 
magnet with only one pole. A steel bar may have more than 
two poles, ^| 40, but always, at least, two opposite poles. 

8. Magnetic Substances. — There is a distinction between 
magnets and magnetic substances. A magnet attracts only at 
its poles, each of which possesses opposite properties. A piece 
of iron will attract a magnet, no matter what part of it is ap- 
proached to the magnet ; it does not possess fixed poles or a 
neutral point, while a magnet has at least two poles, one of 
which always repels one pole of another magnet. 

9. Magnetisable Metals. — The magnetic metals used in 
practice are steel and iron. Beside these, the metals nickel, 
cobalt, chromium, and cerium are attracted by a magnet, 
but only very feebly. Nickel and cobalt are the best of this 
class, but are very inferior to iron or steel. For practical 
purposes all other substances such' as copper, lead, gold, 
platinum, wood, rubber, glass, etc., may be regarded as un- 
magnetisable, or non-magnetic substances. Magnetic attraction 
or repulsion will, however, take place through these substances. 

10. Classification of Magnets. — 
yr , f Natural — The lodestone. 

j Artificial — Steel rubbed with lodestone. 
a fifi • ] ( Permanent — Steel bar magnet. 
-jyj- , -j (Iron under the influence of a per- 

' (. T j manent steel magnet. 

m P rary -j Electromagnet — Iron magnetised by 
^ an electric current. 

QUESTIONS. 

1. What is a natural magnet? 

2. What three important properties does it possess? 

3. How would you locate the poles on a natural magnet ? 



MAGNETISM. 5 

4. Distinguish between a natural and an artificial magnet. 

5. You are given two similar bars of steel, only one of which is 
magnetised. What tests would you apply to determine which one 
is magnetised ? 

6. Define a magnet. 

7. State the law regarding magnetic attractions and repulsions. 

8. How would you prove that a magnet must always have at least 
two poles ? 

9. What is the difference between a magnet and a magnetic 
substance ? 

10. Describe how you would magnetise a sewing needle with a piece 
of lodestone. 

11. What do you mean by polarity ? 

12. A bar magnet is floated on a cork, the N-end is toward the 
observer. What occurs when a S-pole is approached to the S-end of 
the floating magnet? What effect when the N-end is approached to 
this same end ? 

13. What is the difference between a permanent and a temporary 
magnet ? Give an example of each class. 

14. You are given a hard steel bar with a notch filed at one end. 
How would you magnetise it by using the N-pole of a magnet so that 
the notched end would have a N-pole ? 

15. A number of steel needles are inserted vertically into an equal 
number of corks which are then floated in a jar of water with the eyes 
of the needles upwards. How will the needles behave when the 
N-pole of a bar magnet is approached to them ? 

16. Suppose that the eyes of the needles in question 15 are of 
S-polarity, how will they act when the S-pole of a magnet is 
approached to them ? 

17. What two tests would you apply to prove that although a piece 
of iron attracts the N-pole of a suspended bar magnet yet it is not 
itself a magnet? 

18. Give a general classification of magnets, citing an example to 
illustrate each class. 



LESSON II. 

MAGNETISATION. 

To Make an Artificial Magnet — Magnetising Each Half Separately — 
Magnetisation by Divided Stroke— Magnetisation by an Electric 
Current — Magnetisation by an Electromagnet — Making Perma- 
nent Steel Magnets— Compound or Laminated Magnets— Horse- 
shoe Magnets — Horizontal Magnetic Needle — Magnetic Dip 
Needle— Questions. 

11. To Make an Artificial Magnet.— Secure a piece of hard-tem- 
pered steel (about 6 r/ x \ ff x \") and mark one end with a file, which 
will be the N-pole. Place the steel on a table and, beginning at the 
unmarked end of the steel bar, stroke its entire length with the south 
end of a strong artificial magnet. Lift the magnet clear at the end 
and return again for a second stroke in the direction of the dotted line 

and arrows in Fig. 6. Stroke it about ten 
^_ times in this manner and then repeat a simi- 

mm lar stroking process on the other three sides 

III of the bar. Plunge the newly made steel 

,~- *->& n magnet into filings or small tacks, and note 

J'' \ the distribution of magnetism. Suspend it 

\ horizontally in the stirrup and observe 
l whether the marked end points toward the 

___ w J north when it comes to rest. Note that the 

g=r=L— ~~~" **$ N-pole in the magnet you have made was 

" l """"""""""""""""" 1 1 * always touched last by the S-pole of the 

Fig. 6.-Single Stroke, magnetising magnet. One pole always in- 
duces the opposite pole in any magnetisable 
body at the point which was touched last 
by the S-pole of the magnet. One pole always induces the opposite 
pole in any magnetisable body at the point where the pole last leaves 
that body. \ 36. 

12. Magnetising Each Half Separately. — A better 
magnet will be obtained by magnetising each half separately, 
as illustrated in Fig. 7. Stroke one-half of the steel bar with 
the S-pole, beginning at the centre and following the direc- 
tion of the dotted line. Repeat this a number of times on 
each side ; then using the N-pole, stroke the other half in 
the same way. A horseshoe-shaped magnet can be used to 
magnetise another piece of steel by stroking in the direction 

6 



MAGNETISATION. 7 

of the arrows, as in Fig, 8. In stroking the opposite side, 
the same limb of the horseshoe must be brought into contact 



s*~^ 



XD, 



B 



Fig. 7.— Magnetising Each Half Separately. 

with the same pole, as before. A piece of soft iron laid 
across the ends of the horseshoe while being magnetised will 
give better results. 

13. Magnetisation by Divided Stroke.— Place the steel 
bar to be magnetised on two 
other bar magnets, as shown 
in Fig. 9. Take two addi- 
tional magnets, one in each 
hand, with the polarities in- 
dicated, and proceeding 
from the centre, with unlike 
poles, stroke towards the 
ends in the direction of the 
dotted lines. Turn the bar 
over and repeat the opera- 
tion about ten times on each 
side. 

14. Magnetisation by an Electric Current. — If a num- 
ber of turns of insulated wire be wrapped around the steel bar 




Fig. 8. — Magnetising a Horseshoe 
Magnet. 




Fig. 8.— Magnetisation by Divided Stroke. 



8 PRACTICAL ELECTRICITY. 

to be magnetised, and a strong current of electricity passed 
through the coil from a battery or dynamo, as in Fig. 10, the 
steel will be permanently magnetised with a N and S-pole, 
after the current is turned off. Tapping the end of the steel 
with a hammer, while it is under the influence of the current, 
will produce better results. Instead of winding the wire 
around the bar, the bar can be inserted in a spool containing 
many turns of insulated wire (such as EM, Fig. 11, which can 
be slipped off of its iron core) when a stronger magnet will 




Fig. 10. — Magnetisation by an Electric Current. 

be obtained. In making a horseshoe magnet by this 
method insert one limb all the way in the spool ; turn on the 
current ; tap it ; turn off the current ; remove this limb, and 
insert the other limb in the opposite end of the coil and 
repeat the operations. You will now have a magnet, the 
strength of which, until the saturation point of the steel is 
reached, will depend on the current strength, and the number 
of turns of wire on the spool. 

15. Magnetisation by an Electromagnet. — A bar electro- 
magnet (i. e., the above spool and its iron core) may be sub- 
stituted for the permanent steel magnets used in the previous 
methods for making a magnet, or two bar electromagnets 
connected by a piece of soft iron forming a horseshoe elec- 
tromagnet may be used (see Fig. 11.) In this case the cur- 
rent is passed through one spool in one direction, and then 
through the other spool in the opposite direction, when the 



MAGNETISATION. 9 

free ends of the core will have a N and S-pole. One-half of 
the bar to be magnetised can now be stroked over one pole, 



>^T3?4g^. 




Fig. 11. — Magnetisation by an Electromagnet. 

beginning at its middle point and following the direction of 
the dotted lines in Fig. 11, stroke on all sides, and then stroke 
the other half of the bar on the other pole. 

16. Making Permanent Steel Magnets.— The artificial 
magnets in paragraphs 2 and 11 are called permanent mag- 
nets because they retain their magnetism permanently, to a 
certain extent, after magnetisation. Some qualities of steel 
which possess good machine tool properties are not adapted 



Fig. 12. — Round Bar Magnet. 

to making good permanent magnets. Steel containing a 
certain percentage of manganese cannot be magnetised, while 
some brands of cast steel, spring steel, and mild plate steel 
are readily magnetised, but do not retain their magnetism 



10 



PRACTICAL ELECTRICITY. 




Fig. 13.— Student's Bar Magnet Set. 



permanently. Jessop's steel is well adapted to making good 
permanent magnets. Select a piece of good, close-grained, 
rolled steel that has not been heated since it was made and 

cut it (about 6"Xj"xj" 
or 12"xl"x T y). Tem- 
per the steel glass-hard 
by heating it to a moder- 
ately bright red tempera- 
ture and then plunging 
edgewise into water or 
oil. It will become very brittle and can be magnetised by 
any of the methods hereafter given. A permanent magnet 
will have its strength materially weakened if subjected to 
shocks or blows, a high temperature, or brought carelessly 
into contact with the poles of other strong magnets. 

17. Compound or Laminated Magnets.— If a thick piece 
of steel be magnetised and then placed in an acid bath (such as 
nitric acid) for some time, whereby the outer surface is eaten 
off, and then tested for mag- 
netic qualities, it will be 
found to be almost entirely 
demagnetised. From this 
experiment it is inferred 
that the magnetism has 



BC 

-(TV. 



Fig. 14. — Compound Bar Magnet. 



only penetrated the surface of the steel. If a permanent 
magnet then be made up of a number of thin pieces of steel, 
magnetised separately, and fastened together with like poles 
at the same end, it will be stronger than one of solid steel of 
the same dimensions, because it is more thoroughly magnet- 
ised. Such magnets can be made in any form and are known 
as compound or laminated magnets. 

18. Horseshoe Magnets. — When a straight bar of steel is 
bent into the form of a horseshoe, and then properly magnet- 

Fig. 15.— compound Magnet with Soft Iron Pole Pieces. 

ised, the end of one limb will be a N-pole and the other a 
S-pole. By bringing the poles close together in this manner, 
the magnet will lift, or attract much more than the sum of 




MAGNETISATION. 



11 



the attractive forces when used separately ; because, in a bar 
magnet only one pole could be used at a time, while now 
both poles act together. A piece of soft iron, called the 
' ' keeper," ' is placed across the ends of the 
poles when they are not in use, to assist 
in preventing the loss of magnetism. 
Fig. 16 illustrates a horseshoe magnet of 
rectangular cross section with its keeper 
attached. Fig. 13 illustrates the proper 
method of putting away two bar mag- 
nets with their keepers, to prevent loss of 
magnetism ; the unlike poles are placed 
at the same end, with the keeper connect- 
ing them. A laminated, or compound 
horseshoe magnet, built up of a number 
of separate horseshoes and fastened to- 
gether with their like poles at the same end, is depicted 
in Fig. 17. Laminated horseshoe magnets are used in elec- 
trical measuring instruments, magneto-electric generators, and 
in telephones. 

19. Horizontal Magnetic Needle. — The magnetic needle 
with its stand is shown in Fig. 18. It consists of a thin 




Fig. 16. — Horseshoe 
Magnet and Keeper. 






Fig. 17. — Compound 

Horseshoe Magnet 

With Keeper. 



Fig. 18. — Horizontal Magnetic 
Needle. 



piece of magnetised steel in the form of an elongated lozenge, 
in the centre of which a hole has been drilled, and a glass, 
agate, or brass V-shaped jewel affixed, so that the needle 



12 



PRACTICAL ELECTRICITY. 



will swing freely when poised on a hardened steel point. 
The needle takes up a position N and S when at rest similar 
to the suspended bar magnet. Sometimes the needle 
is suspended from a vertical support by a cocoon silk 
fibre, in which case it is much more sensitive, due to ■ the 
elimination of the friction in the poised form. Both types 
are much used commercially in electrical detecting and 
measuring instruments, as in the mariner's compass, galva- 
nometers, etc. 

20. Magnetic Dip Needle.— This needle is made in the 
form of a lozenge, similar to the horizontal needle, but it is 
poised or suspended by means of a shaft running through the 




cHH 3 



Fig. 19. — Magnetic Dip Needle. 



Fig. 20. — Magnetic Dip Needle. 



centre of the lozenge at right angles to it, and is held in posi- 
tion b}' brass V centres, or agate bearings, as shown in Figs. 
19 and 20. It is thus free to turn vertically. In some types 
the cradle holding the horizontal shaft is poised on a steel 
needle, or swung by fibre suspension. The needle is thus 
free to take up a position N and S, and to incline on its 
axis. The principle and use of the dipping needle is ex- 
plained in ^j 52. 

QUESTIONS. 

1. How would you magnetise a steel sewing needle by the method 
of magnetising each half separately, so that the eye would be a 
N-pole ? Give sketch. 

2. How would you magnetise a steel horseshoe magnet by the 



MAGNETISATION. 13 

" Divided Stroke Method " so that the marked end would be a N-pole ? 
Give a sketch to illustrate your answer. 

3. AVhat is an electromagnet ? 

4. Given a coil of wire, a battery, and a piece of iron, how would 
you magnetise the iron ? AVhat kind of a magnet would it be after 
the circuit was disconnected ? 

5. How would you magnetise a steel horseshoe by an electro- 
magnet ? Suppose you only had a coil of wire connected to a battery, 
how then would you proceed ? 

6. What kind of steel would you select to make a good, permanent 
magnet ? 

7. What care is necessary in handling permanent magnets ? 

8. AVhat is a compound magnet ? How would you put four horse- 
shoe magnets together to make a compound magnet? 

9. What is the advantage of laminated magnets over those made 
from solid steel ? 

10. Describe a horizontal magnetic needle. For what purpose is it 
used? 

11. AVhat is a dip needle? How does it differ from a horizontal 
needle ? 

12. Show by a sketch how three bar magnets should be put away 
without keepers, so that they would retain their magnetism. 

13. A laminated permanent magnet is constructed of four strong 
bar magnets but appears to be very weak. What do you suppose the 
trouble is, and how would you prove the supposition ? 

14. A piece of hard steel, bent in the form of a U, is to be mag- 
netised so that both ends will have N-polarity. Illustrate by a sketch 
how you would proceed to magnetise it by the "divided stroke" 
method, using four permanent magnets, and indicate all the polarities. 

15. How would you magnetise a steel pen, using a horseshoe mag- 
net, so that the point would be a N-pole? Give two tests you would 
make to prove that you had magnetised it correctly. Make sketch. 



LESSON III. 



MAGNETIC FIELDS. 



Magnetic Force — Magnetic Lines of Force — The Magnetic Field — 
Making Magnetic Fields — Axis and Equator of Bar Magnet — 

Questions. 

21. Magnetic Force. — The force exerted by one magnet 
on another, to attract or repel it, or to attract iron filings, or 
pieces of iron, is termed magnetic force. It is not perceptible 
to any of the senses. When the magnet has been plunged 
into filings, the space thus occupied is shown to be perme- 
ated with the force, and the filings serve as a useful indicator 
to show the nature of the force and its direction and distribu- 
tion in the space surrounding the magnet. The magnetic 
force is not the same at all distances, but decreases as the dis- 
tance from the magnet increases. The attractive force 
between a magnet and a piece of soft iron is mutual, that is, 
the iron attracts the magnet just as much as the magnet 
attracts the iron. This may be illustrated by suspending a 
piece of iron in a stirrup, as in Fig. 3, and noting the dis- 
tance at which it is attracted by a magnet, and then sus- 
pending the magnet and permitting the iron to occupy the 
previous position of the magnet ; or the magnet may be 
floated on a cork in a jar of water, and it will be equally 
attracted by the piece of iron. 

22. Magnetic Lines of Force. — The magnetic force ema- 
nates in all directions from a magnet. To ascertain the 
direction of the force in the space surrounding a magnet, a 

1 X^-t'^X I 



Fig. 21. — Exploring the Magnetic Field with a Dip Needle. 

14 



/ 



\ 



y 



MAGNETIC FIELDS. 15 

small dipping needle, as in Fig. 21, or a magnetised sewing 

needle suspended by a thread from its centre, as in Fig. 22, 

may be used. With the bar magnet flat on the table, place 

the exploring needle a 

short distance above the 

magnet, midway between 

its two poles. The nee- N^ 

die takes up a position 

parallel to the magnet, i " ^vy*- > u . ^s^^^^Y*'? '' «J 

with its N and S-poles S 1 \^U J^ '/ \ 

attracted by the unlike * ' 

poles of the magnet, the Fig. 22.— Exploring the Magnetic Field, 
attractions of the poles 

being equal. Now move the dipping needle a little to the 
right of the middle position, and it inclines to the magnet, 
the angle of inclination increasing as you approach the 
pole, till it becomes vertical at the pole ; if carried past 
the end of the bar it still inclines to the pole, indicating 
by its resultant position the direction of the magnetic 
force at this point. In a similar manner the dipping 
position underneath the magnet may be noted. Place the 
magnet on a sheet of paper and make a similar exploration 
of it with your suspended needle. Mark with a pencil on 
the paper a dot and X to represent the N and S-pole of the 

needle when it comes to rest 

j*********^* f° r each particular position. 

jf* \ + A line may then be drawn 

> \ connecting each dot with its 

£ u \ X, and the direction of the 

magnetic force around the 

magnet will be illustrated 

graphically in the form of a 

\ 8 J curve similar to Fig. 23. 

V f From these experiments it is 

\ / deduced that magnetic force 

*\, ^ is exerted in all directions 

from a magnet. In similar 



Fig. 23 —Plotting Needle's Position, manner, another series of po- 
sitions could be taken about 
one-eighth inch farther distant from the magnet, and another 
carve indicating the direction of the magnetic force obtained. 
The entire space surrounding the magnet for a considerable 



16 



PRACTICAL ELECTRICITY. 



T.B. 



distance from it will thus be found to be permeated with 
magnetic lines of force. Similar explorations made on the 
other side of the magnet will give the same results. 

23. The Magnetic Field. — The space which is permeated 
by the magnetic lines of force surrounding a magnet is con- 
ventionally called the magnetic field of force, or simply a 
magnetic field. It is also assumed that the magnetic lines 

of force emanate from the 
N-pole of a magnet, pass 
through the surrounding 
medium, re-enter the S- 
pole and complete the 
path, or circuit from the 
S-pole to the N-pole, 
through the magnet it- 
self. Every line or curve 
of magnetic force must 
have a complete circuit; 
hence, as already proven, 
it is impossible to have a 
magnet with only one 
pole. The magnetic lines 
complete their circuits in- 
dependently, and never cut, 
cross, or merge into each 
other. The internal field 
is much smaller in cross 
section than the external field, due to the fact that the steel 
is a much better conductor of magnetic lines of force than 
the surrounding medium. Because of this concentration of 
lines of force inside the magnet they are crowded together 
where they leave the magnet at the N-pole, and where they 
enter at the S-pole. The strong attraction at the poles, and 
none at the middle of the magnet is thus accounted for. 

24. Making Magnetic Fields. — Lay a bar magnet flat 
on a table and cover it with a sheet of cardboard. Obtain 
some sifted iron filings from which the dust has been re- 
moved and enclose them in a pepper-box or piece of gauze 
netting. Sift the filings over the cardboard, while gently 
tapping its edge with a lead-pencil. The filings being mag- 
netic bodies, arrange themselves in the direction of the mag- 
netic curves of lines of force and thus produce a graphical 




Fig. 24.— Coating Paper with Paraffin 
Wax. 



MAGNETIC FIELDS, 



17 



representation of the magnetic field surrounding the magnet, 
as in Figs. 25 and 26. When it is desired to make a perma- 





Fig. 25.— Making Magnetic Field of a Bar Magnet. 

nent record of the magnetic field, a piece of paraffin-coated 
paper is used in place of the cardboard. After the field is 




Fig. 26.— Magnetic Field Between Unlike Poles. 



18 



PRACTICAL ELECTRICITY. 



produced, the flame of a Bunsen burner is gently applied, 
heating the paraffin, which upon cooling fixes the iron fil- 



1 ,' 


1 >' / / *' .-or— ^ *X \ \ \ ; / 


*^-I: 


. N rf Jf&<meticijlzis .^arc, 


*''''-'. 




i 
i 


\V\ \^SS^-'' r '<y''y' ■// j >x 

\ \ \ ^ — --^. — - y ,- ; > 



g>„_ 



Fig. 27. — Bar Magnet. 



ings to the paper. Paraffin paper can be prepared by dipping 
unglazed paper into a tray of melted paraffin. See Fig. 24. 
If the field is produced on sensitized photographic paper and 
then properly exposed to the light, and afterwards developed, 
permanent graphical records will be obtained. The student 
should produce all the cases of fields (Figs. 26 to 33), tern- 




Fig. 28.— Two Parallel Bar Magnets, Unlike Poles Adjacent. 

porarily at least, study each one in detail as it is made, and 
reproduce the same by a sketch at the time it is being made. 



MAGNETIC FIELDS. 



19 




Fig. 29. — Two Parallel Bar Magnets, Like Poles Adjacent. 



/ , 






^ N 



s ss>- 
) rrr. , . ; 






z 



Fig. 30.— Note-book Sketch of Fig. 26. 




Fig. 31. — Repulsion Between 
Like Poles. 



Fig. 32.— Magnetic Field of the 
End of a Bar Magnet. 



20 



PRACTICAL ELECTRICITY 



Many other possible combinations of magnets to produce these 
magnetic figures will occur to the student. A thorough 
knowledge of the direction of lines of force, as depicted by 




Fig. 33. — Magnetic Field of a Horseshoe Magnet. 

the graphical representations of magnetic fields, will greatly 
assist in the understanding of the phenomena of electro- 
magnetism and electromagnetic induction, to be considered 
later. 

25. Axis and Equator of Bar Magnet.— The straight 
line joining the N and S-poles of a bar magnet is called the 
magnetic axis (Fig. 27). A line drawn through the neutral 
point at right angles to the axis is called the magnetic 
equator. The neutral point may be defined as the position 
midway between the poles where by the aid of iron filings 
ho external magnetism is shown. 



QUESTIONS. 

1. What is magnetic force ? How would you prove its existence 
and direction around a magnetised steel bar ? 

2. How would you prove that a piece of iron attracts a magnet just 
as much as the magnet attracts the iron ? 

3. Give, your idea of magnetic lines of force and state how you 



MAGNETIC FIELDS. 21 

would explore these lines around a bar magnet. Illustrate your 
answer by a sketch. 

4. What is a magnetic field? 

5. Describe a process for permanently making magnetic fields. 

6. What is meant by internal and external field? Show by a 
sketch the direction of the lines of force in both. 

7. A piece of steel attracts the N-pole of a magnet. Would this 
phenomenon positively prove that the steel is magnetised? Give a 
reason for your answer. 

8. A bar magnet and a horseshoe magnet are laid flat on a table 
so that their neutral lines form one straight line, N-pole opposing 
N-pole. Sketch the graphical field you would expect to see if iron 
filings were used. 

9. Sketch a bar magnet and indicate its axis and magnetic equator. 

10. Six horseshoe magnets are arranged symmetrically around the 
circumference of a circle with their poles pointing toward its centre. 
The adjacent poles are in the order NS, SN, NS, etc. Make a sketch 
showing the direction of the lines of force as you would expect to see 
them when iron filings are used. 

11. What is meant by the neutral point of a bar magnet? 

12. Illustrate by a sketch the neutral point, and, also, the axis and 
equator of a horseshoe magnet. 

13. Two bar magnets with like poles adjacent are laid on a piece of 
cardboard parallel to each other. A horseshoe magnet is placed so 
that its poles are directly opposite but a little distance from the bar 
magnet's poles. Sketch the resultant magnetic field you would expect 
to see from this combination if iron filings were used. 



LESSON IV. 

THEORY OF MAGNETISM. 

The Nature of Magnetism — Experimental Proof of the Molecular 
Theory of Magnetism — Breaking a Magnet— Magnetic Satura- 
tion — The Magnetic Difference Between Iron and Steel — Reten- 
tivity and Residual Magnetism — Destruction of Magnetism by 
Vibration — Destruction of Magnetism by Heat — Strength of a 
Magnet — Lifting Power of a Magnet — Questions. 

26. The Nature of Magnetism. — What is known as the 

molecular theory of magnetism is offered as an explanation 
of the phenomenon arising from the magnetism of a piece of 
steel or iron. The theory, which is beautifully illustrated by 






•^"V "fi n 



*V 



» 9 * " n s 

Fig. 34. — Possible Arrangements of Molecules (Magnified) . 

the experiments following, assumes that in a bar of steel, 
each of all the individual particles, or molecules which com- 
pose it, is a magnet. If the steel or iron is unmagnetised, 
then the particles arrange themselves promiscuously in the 
steel, but according to the law of attraction between unlike 
poles; the magnetic circuits are satisfied internally, and 
there is no resulting external magnetism. Fig. 34 illustrates 
(highly magnified) several possible positions, in which the 
particles in a solid steel bar may arrange themselves, when 
there is no external magnetism. When the steel bar is 
stroked with a magnet, or placed in a current- carrying coil 
of wire, the particles rearrange themselves according to the 
law of attraction, symmetrically with the axis of the coil, 
thus breaking up the closed magnetic circuits, and so making 
22 



THEORY OF MAGNETISM. 23 

evident external magnetism. An enlarged view of this ar- 
rangement of the particles is shown in Fig. 37. 

27. Experimental Proof of the Molecular Theory of 
Magnetism. — Fill a small glass test-tube with coarse steel 
filings, and insert a cork in the mouth of the tube. Test each 
end separately for magnetism by bringing it near a suspended 
needle. Either end attracts the same pole of the needle, 
proving thereby that it is not magnetised. Treat the tube 
now as a steel bar, and being careful not to shake it, proceed 



Fig. 35.— Glass Tube of Steel Filings Before Magnetisation. 

to magnetise it by any of the methods previously given. 
Test again with the needle; one end repels one of the needle's 
poles and attracts the other pole. Always make a repulsion 
test to prove that a body is a magnet. Now shake the tube 
thoroughly so as to intermingle the filings, repeat the tests 
above, and you find that the tube is no longer a magnet, but 
has been demagnetised. The filings are now indiscriminately 
arranged in the tube with the magnetic circuits of the nu- 
merous small magnets completed through each other, Fig. 



Fig. 36. — Glass Tube of Steel Filings After Magnetisation. 

35; hence no external magnetism. When rearranged in 
the tube under the influence of magnetic force, they assumed 
symmetrical positions, each one lying in line with, or parallel 
to its neighbor, N-pole next to S-pole and so on, Fig. 36. 
The result of this rearrangement of a number of small mag- 
nets would be an accumulation of the lines of force, which, 
when they reached the end of the tube would have no other 
path to complete their circuit ; so that the tube presents the 
characteristics of a bar magnet, Fine particles of magnetic 



24 



PRACTICAL ELECTRICITY. 




oxide of iron (lodestone) mixed with water may be poured 
into a tube. When the tube is shaken it is impervious to light, 

because of the satisfied inter- 
nal arrangement of the mag- 
netic circuits; when placed 
in a coil of wire carrying a 
current the particles rear- 
range themselves longitudi- 
nally so that when viewed 
from the end of the tube 
they offer less obstruction to 
the light. 

28. Breaking a Magnet. — The breaking of a magnet 
further supports the molecular theory of magnetism. Mag- 
netise a long, thin piece of hard-tempered steel, and mark the 
N-pole. Break it in half and test each piece separately. In 
one-half the N-pole remains N, as previously marked, but a 



Fig. 37.— Magnified Position of Steel 
Filings. 



N 



S 



N S N . 6 N S N S 

Fig. 38.— Breaking a Steel Magnet. 

new S-pole is developed, while in the other piece the S-pole 
remains as before and a new N-pole is developed. Break 
these pieces again, Fig. 38, and each part is a perfect magnet, 
with the poles distributed as in the previous case. Break the 



n $ 


it s 


n -e 


n t 


n $ 


n 9 




it f 


it 1 


n $ 


n t 


n i 


n $ 


s 


it $ 


it $ 


H » 


n $ 


n * 


>t e 





N 



Fig. 39. — Magnified Arrangement of Particles in a Bar Magnet. 

remaining pieces until they become too small to be broken, 
testing each one, and every one is still a magnet. The con- 
clusion is, then, that a steel or iron magnet is an aggregation 
of small magnets, arranged in the magnified position shown 
in Fig. 39. 

29. Magnetic Saturation. — We cannot see the mole- 
cules of iron or steel changing their relative positions under 
the influence of magnetism, but these experiments are in- 



THEORY OF MAGNETISM. 25 

tended to show what probably takes place when steel or iron 
is magnetised. According to the theory, the magnetised iron 
or steel has its molecules irregularly disposed, as the steel 
filings were in the tube when shaken. Magnetisation turns 
them around on their axes until they are arranged symmet- 
rically. When they have all been turned around the bar is 
said to be saturated, or completely magnetised ; it cannot be 
further influenced by magnetism, however strong the force. 

30. The Magnetic Difference Between Iron and Steel 
— Retentivity and Residual Magnetism. — Magnetise a bar 
of steel by insertion in a coil carrying a current of electricity, 
and then a bar of soft wrought iron of the same dimensions. 
Test the attractive power of each by nails or filings, while 
the current is on, and it is found that the soft iron possesses 
the greater attractive force. When the current is off, the steel 
possesses far superior attractive properties to the iron, which 
it retains, for the most part, permanently. The soft iron is 
magnetised very slightly. The magnetism remaining in the 
iron is known as residual magnetism, and is a most import- 
ant factor in operating dynamos, since upon it their self-ex- 
citing properties depend. The molecules of iron and steel 
offer some resistance to the force tending to turn them on 
their axes. The resistance of the steel molecules being much 
greater, it is difficult to turn them around, but on being once 
turned around it is equally as difficult for them to turn again 
to their original position due to the intermolecular friction ; 
hence the resulting permanent magnetism. On the other 
hand, the molecules of soft iron turn very readily when under 
the influence of a magnetic force, but assume their original 
position when the influencing force is removed, as the in- 
ternal molecular friction is much less, thus accounting for 
the temporary magnetism in iron. That the particles do not 
regain their exact original position is shown by the slight 
trace of magnetism, called residual magnetism, always found 
in any piece of iron after having been magnetised. The 
power to retain magnetism is called retentivity. The greater 
the retentivity of a magnetisable body, the more resistance it 
offers to being magnetised ; hence, we see why it is more 
difficult to magnetise a piece of hard steel than one of soft 
iron. 

31. Destruction of Magnetism by Vibration. — Magnet- 
ise a piece of soft iron bar and carefully test its polarity by 



26 PRACTICAL ELECTRICITY. 

the needle. Holding it in the hand, pointing east and west, 
strike the end several blows with a brass or wooden mallet. 
Upon again testing, you find its qualities as a magnet have 
been entirely destroyed. You have assisted the few remain- 
ing molecules to assume their original position, or you have 
demagnetised the bar. Slight shocks are sufficient to demag- 
natise soft iron ; steel retains with tenacity the properties of 
a magnet, but its magnetic strength is impaired by shocks or 
vibrations ; hence, electrical instruments containing perma- 
nent steel magnets should be handled Avith care. Good bar 
magnets should not be dropped on the floor or table. Many 
practical uses are made of the qualities of soft iron with re- 
spect to the ease with which it can be magnetised and de- 
magnetised. Telegraph sounders and the soft iron armature 
cores in dynamos, are magnetised and demagnetised many 
hundred times in a minute. 

32. Destruction of Magnetism by Heat. — Magnetise a 
thin strip of steel. Test its polarity. Heat the strip in a 
Bunsen flame to a bright red color ; permit it to cool, and 

repeat the polarity tests. It is 
found to be entirely demagnet- 
ised. Suspend a small piece of 
soft iron by a brass chain, heat 
the iron with a flame, and 
approach to it a bar magnet. 

f* 1|| f:. m . £M\ The iron is not attracted until 

\ N |f|| \0mim it becomes cool. Heat is a 

^fHP^ mode of molecular motion ; that 
Fig. 40.-Ked Hot Iron Ball is IS, it sets in vibration the parti- 
Non-Magnetic, cles of the magnetised steel 
strip, and assists them to satisfy 
their original internal magnetic condition. On the other 
hand, it has been found that magnets have their strength 
increased when subjected to very low temperatures. 

33. Strength of a Magnet. — The strength of a magnet is 
the amount of free magnetism at the poles, and is not the 
same as the lifting power, which is dependent upon the shape 
of the poles as well as upon the shape and quality of the 
body to be lifted. The strength of a magnetic pole is, there- 
fore, measured by its action on another pole at a distance. 
If one bar magnet repels a magnetic needle, with twice the 
force of . repulsion as that due to another magnet placed at 




THEORY OF MAGNETISM. 27 

the same distance from the needle, we would say the strength 
of the first magnetic pole was twice that of the second mag- 
netic pole. In magnetic measurements a unit strength of 
pole is adopted by which the strength of any other pole can 
readily be compared. 

34. Lifting Power of a Magnet. — The lifting or porta- 
tive power of a magnet depends on the strength and form of 
the magnet. Small magnets lift more in proportion to their 
weight than large ones. A horseshoe magnet will lift three 
or four times as much as a bar magnet of equal weight. A 
long bar magnet will lift more than a short one of equal 
weight. A magnet with rounded or chamfered ends will lift 
more than one of the same weight with ends dressed square, 
even though they are magnetised equally. If a horseshoe 
magnet has a little weight added to it daily it will be found 
to attract considerably more than would have been possible if 
the weight had been originally added. When this weight 
becomes excessive, so that the armature is detached, the 
magnet's strength falls to its original value. This growth of 
the lifting power is a curious and unexplained phenomenon. 
Electromagnets may be so powerfully magnetised as to 
require a force of 200 pounds per square inch to separate the 
keeper from the magnet's poles. 

QUESTIONS. 

1. Explain what you understand by the molecular theory of mag- 
netism. Give sketches. 

2. Sketch several possible positions of the molecules in an unmag- 
netised piece of steel. 

3. What is meant by a magnetically satisfied condition? Give 
sketch. 

4. Sketch the position of iron filings in a test tube before and after 
it has been magnetised. 

5. How would you experimentally prove your idea of the molec- 
ular theory of magnetism ? Give sketch. 

6. A magnet is broken into five pieces. Sketch the pieces and 
their resultant polarity in the order in which they were broken. 

7. Explain how, by successively breaking up a bar magnet, you 
support the molecular theory of magnetism. Give sketch. 

8. According to the molecular theory of magnetism, explain what 
you mean by magnetic saturation. 

9. Why is it that hard steel makes a better permanent magnet 
than soft iron ? 

10. What do you understand by retentiyity ? OUye an example to 
illustrate your answer, 



LESSON V. 



MAGNETIC INDUCTION. 







Magnetic Induction Experiments -Magnetic Induction — Action and 
Keaction Equal and Opposite — Magnetic Inductive Effect of Like 
and Unlike Poles — Reversed Polarity — Consequent Poles — Mag- 
netic Screens — Questions. 

35. Magnetic Induction Experiments.— (1) Separate a piece of 
soft iron bar from a magnet by a piece of paper or wood, as in Fig. 41. 
Plunge the iron into filings; it attracts many more filings while 
under the influence of the bar magnet than it would do otherwise. 
It is a temporary mag- 
net made inductively 
by the influence of a 
permanent magnet. 

(2) Hold the bar 
magnet vertically with 
one end in contact with 
an end of the iron. 
Plunge the other end 
of the iron again into 
filings. It now attracts 
more filings than be- 
fore. Magnetic induc- 
tion thus takes place 
between bodies in con- 
tact or separated from each other. Interpose between the adjacent 
ends of the magnet and iron bar pieces of brass, lead, glass, rubber, 
copper, etc. The filings are attracted to the same degree, when the 
same distance is maintained, as when these bodies are not interposed. 

(3) Support a piece of iron rod about eight inches long, horizontally, 

in line with, and on the same 
height, as a poised magnetic 
needle, when it is pointing 
toward the N and S, as in 
Fig. 42. Leave a small dis- 
tance between the end of the 
iron rod and the N-pole of 
the needle. The N-pole of 

Fig. 42.— Magnetic Induction. the needle induces a S-pole 

in the iron nearest to it, 
and a N-pole at the far end, and is attracted to the bar by the phe- 
nomenon of magnetic induction. With the N-pole of a bar magnet 
approach the far end of the iron rod, and the needle is repelled away 
28 



Fig. 



Iron Filing* 
41. — Magnetic Induction. 




■£nt4*3~ ■xu/S&ubJl* 



MA GNETIC IND UCTION. 29 

from the iron rod. The bar magnet, (the inducing body) being 
stronger than the needle, induces a S-pole in the end of the iron 
nearer to it, and a N-pole in the other end ; thus not only neutraliz- 
ing the needle's inductive effect, but demagnetising the iron, and 
magnetising it again in the opposite direction. When the magnet- 
ising body is removed the needle assumes its former inductive posi- 
tion, provided that the iron is very soft. This experiment proves that 
the iron has poles when inductively magnetised. To prove that the 
bar magnet is not repelling the needle, repeat the test without the 
iron bar interposed and with the magnet at the same distance, when 
the needle will be only slightly deflected. 

(4) The amount of deflection will not be altered in the above ex- 
periment when pieces of non-magnetic bodies are interposed. Inter- 
pose a text-book while the needle is repelled, and the repulsion is 
exactly the same as before. 

36. Magnetic Induction. — A piece of soft iron, when 
placed in the magnetic field of another magnet, becomes 
itself a temporary magnet, having at least two unlike poles, 
and a neutral point. The iron is the body under induction, 
the magnet the inducing body, and the phenomenon known 
as magnetic induction. It may be defined as the action and 
reaction which occur when the magnetic lines of force, ema- 
nating from a magnetic body, make evident the latent mag- 
netism in another magnetic body, either with or without 
contact between them. Magnetic induction, therefore, takes 
place when the body is in contact with, or separate from the 
inducing bod} 7 . The phenomenon of magnetic induction 
always precedes the attraction of a magnet for a magnetic 
body, and takes place through all non-magnetic mediums, 
whether they are solids, liquids, or gases. One pole induces 
the opposite pole at that part of the body under induction 
nearest to the inducing pole, and a like pole at the most 
remote point. Magnetic induction in iron may be explained 
by the molecular theory, when it is remembered how readily 
the molecules of soft iron turn on their axes when subjected 
to the lines of force of a magnetic field. Each individual 
iron filing becomes a magnet by induction before it is 
attracted, and when attracted, acts inductively on its neigh- 
bor in the same manner. The methods given in paragraphs 
12, 13, 14, etc., for making magnets are based on the prin- 
ciple of magnetic induction, which the student should now 
apply to each case. 

37. Action and Reaction Equal and Opposite. — Bring 
the end of a piece of unmagnetised steel near to one of the 



30 PRACTICAL ELECTRICITY. 

poles of a poised needle, approaching from an eastern or 
western direction, as in Fig. 43, the needle is deflected from 
its original position toward the steel. It induces an unlike 
pole in the end of the steel nearer to it, and a like pole 
at the other end. The two unlike poles attract' each 
other. The steel bar tends to move ^ e 

toward the needle, but is not free to || 

move ; the needle can and does move. <§,£ 

The unmagnetised steel bar thus be- rwgn^ ;«rf ^ 
comes a magnet before the needle / " Hard "s'teei " " 
can be attracted to it. A piece of \ 
soft iron of the same size and at the \ 
same distance, will produce a greater . \ 
deflection of the needle than the *fev 

steel, because it is more readily v^>s^ 

magnetised. Comparative tests can *%^j 

thus be made of the susceptibility of „. „ ,, 

different specimens of iron and steel ^g. 43-Needle Attracted, 
to the same magnetising influence. There is in all such cases, 
first, the inductive action of the needle's magnetism on the bar, 
and then the reaction from this induced magnetism upon the 
needle, causing it to be deflected. The action being greater 
upon soft iron than upon steel, the reaction is also greater. 
In all cases of magnetic induction the action and reaction are 
equal and opposite. As there is a stronger magnetic field 
(a greater number of lines of force) near the needle than at a 

short distance from 
it, the less the dis- 
tance between the 
inducing body and 
that under induc- 
tion, the greater will 
be the inductive 
action. By placing 
the bars, one on 
each side of the 
same pole of the magnetic needle and at right angles to it 
and moving the iron bar away until the needle is balanced 
in a N and S direction, as in Fig. 44, you can prove by the 
greater distance of the iron than the steel bar from the 
needle that the former is more susceptible than the latter to 
magnetic induction. 



"Unman» e t>s 


v7 

— «y. 


*, 
N 








J» 


>-- -|#— - 





-4, 


j, JfarJSkr 


> 


Soft 


Iron 


J 


4^ 


'•"rV"*" 




^,—-H^ 


$£* 




Fi 


R. 44. 


— Needle Balanced. 







MAGNETIC INDUCTION. 



31 



Y 



Demagnetising Inductive Effect 
of an Unlike Pole. 



1£L 






D 



38. Magnetic Inductive Effect of Like and Unlike 

Poles. — Suspend from a horizontally supported bar magnet 

three soft iron nails, one below 

*n*z — , the other, as depicted in the 

j gg* 8 fl g first diagram of Fig. 45. The 

resulting inductive effects of the 
bar magnet on the nails is in- 
dicated by the polarities marked 
to the left of the nails. Each 
nail head has induced in it a 
S-pole, while all the points are 
N -poles. Now slide over the 
top of the bar magnet the un- 
like or S-pole of a similar mag- 
net. The resultant inductive 
polarities due to this magnet 
are marked to the right of the 
nails. This second magnet in- 
duces a N-pole at the head of 
every nail, and a S-pole at every 
point. The result is a demag- 
netising inductive effect upon the 
nails, so that their magnetism 
being neutralized, they drop off 
by reason of their own weight. 
The same chain of demagnetis- 
ing inductive effects will occur 
if a like, or N-pole, is brought 
up from underneath the sus- 
pended nails. (See second dia- 
gram.) In the third diagram 
of Fig. 45 a like, or N-pole, is 
moved over the top of the mag- 
net, and its inductive effect upon 
the nails is to reinforce the mag- 
netism already at each nail head 
and point, so that more nails 
may now be added. The in- 
creased magnetising inductive 
effect will also be noted if an 
unlike pole is brought up from 
underneath, as in the last dia- 



Demagnetising Inductive Effect 
of a Like Pole. 



SJ% 



Increased Magnetising Inductive 
Effect of a Like Pole. 



3 



BE 



;HJ 



Fig. 45. — Increased Magnetising 

Inductive Effect of an 

Unlike Pole. 



32 PRACTICAL ELECTRICITY. 

gram. Two magnets thus placed, with their like poles 
together, will not support twice as many nails as one magnet, 
for although they act unitedly upon the nails, they are, in a 
measure, opposing each other. For this reason also com- 
pound magnets are not so strong as the sum of the strengths 
of the individual magnets of which they are composed. 

39. Reversed Polarity. — If two like poles of a strong and 
weak magnet be approached to each other, as a compass needle 
not free to move and a bar magnet, repulsion will take place 
up to within a certain distance between the like poles, after 
which attraction occurs. Then the inductive effect of the 
stronger magnet has demagnetised the less powerful magnet, 
and remagnetised it again oppositely, or as we say, reversed 
its polarity. Magnetic needles often have their polarity thus 
reversed, so that the marked end points S instead of N. In 
making any tests with a needle always allow it to come to rest first 
in the earth's field, as the polarity may have been reversed since it 
was last used. 

40. Consequent Poles. — With a reversal of polarity some- 
times more than two poles are manifest in the body having its 
polarity reversed. In such cases the body will have a number 
of intermediate poles and neutral 
points, which may be readily 
shown by plunging its entire length f ,. 
into iron filings. Such inter- N \ ! (9/:--?vvS ; ^^'/^^^/.o 
mediate poles are called consequent 
'poles and arrange themselves as 
shown in Fig. 46. A bar thus 
magnetised practically consists of 
several magnets put together end 
to end, but in the reverse order Fi 46> _ Consequent Po ie S . 
NS, SN, NS, etc. The nature of 

each pole can be tested, while it is attracting iron filings, 
by bringing near it a bar magnet with some filings attracted 
to it. The attraction or repulsion between the filings can be 
noticed at a considerable distance. 

41. Magnetic Screens. — Permit a magnet to deflect a 
magnetic needle from its N and S-position ; the deflection is 
not altered, if any non-magnetic substance be interposed 
between the needle and the magnet, such as a piece of wood, 
glass, or rubber, Fig. 47. The needle's lines of force com- 
plete their circuit through the non-magnetic body to the mag- 




MAGNETIC INDUCTION. 



33 



net, as shown in Fig. 47. A piece of iron, however, when inter- 
posed between the magnet and the needle, acts as a magnetic 
screen and reduces the deflection of the needle toward the mag- 
net. A needle, free to move, takes up a position in the earth's 
magnetic field with its magnetic lines parallel with, and in 
the same direction as the earth's lines of force. When a 
magnet is approached to it, it assumes a position which is 
the resultant of the two forces now acting upon it. No effect 
is produced by interposing a non-magnetic body, such as a 
board, but when a piece of iron is interposed part of the 
lines of force of the magnet (Fig. 48) are now employed in 



. s To HQSSSlk&Poh vn 
if,- - "/ ~S~\ 



& 


f 


>*"" 


~"-^ 


N, 




is 










N 




V 


v... 




_*■' 


/ 




Fig. 47. — Needle Deflected Through Non-Magnetic Body. 



magnetising the iron plate by induction. The needle pro- 
duces a similar effect on the other side of the plate, and being 
free to move, deflects slightly, until its lines of force are pro- 
portionately accommodated between the earth's magnetism 
and the magnetism of the iron plate. When a thick iron 
plate is used it forms a perfect shield to the needle against 
the action of the bar magnet. If a compass needle were 
placed in the centre of a thick iron sphere it would be 
entirely screened from any external magnetism. This prin- 
ciple is utilized in the manufacture of heavy cast-iron boxes 
3 



34 



PRACTICAL ELECTRICITY. 



for measuring instruments which are to be placed on switch- 
boards near magnetic fields. Watches are often inclosed in 
a hunting case made of soft iron to protect their steel main 
springs from becoming magnetised from any cause. Should 



K 



vA 






M 






!? 



% 




HP*. 

Fig. 48. — Needle Screened from Magnet by a Magnetic Body. 



the spring become magnetised the watch generally runs slow, 
due to the force of attraction between the poles of the spring. 
Non-magnetic bodies are employed in the springs of non- 
magnetic watches. 

QUESTIONS. 

1. Cite and illustrate by sketches an experiment to illustrate the 
phenomenon of magnetic induction. 

2. A bunch of sewing needles is suspended by a thread passing 
through the eyes, above the N-pole of a bar magnet. State three 
magnetic phenomena which take place. Give sketches. 

3. How do you explain the phenomenon of magnetic induction by 
the molecular theory ? 

4. Apply the principle of magnetic induction to a piece of steel you 
are required to magnetise by rubbing it from one end to the other 
with one pole of a bar magnet. Give sketches illustrating the stages 
of magnetisation. 

5. A piece of iron and then steel are each held three inches from 
a poised needle. Which piece will deflect the needle most, and why ? 

6. Give sketches illustrating four cases of the increased and de- 
creased magnetic inductive effect, of like and unlike poles, of two bar 
magnets. 



MAGNETIC INDUCTION. 35 

7. A magnetic chain of steel pins is formed from one of the poles 
of a bar magnet. When the chain is removed from the pole it still 
remains intact. How do you account for this ? Give sketch. 

8. A chain of soft iron nails is made from the pole of a magnet. 
Upon attempting to remove the chain all the particles of iron separate 
from each other. Give sketch and explanation. 

9. A compass is supposed to have its polarity reversed. What do 
you understand by this ? 

10. How would you correct the reversal of polarity in a compass 
with two bar magnets so that the arrow head would point N ? You 
cannot get at the needle to stroke it, but there is a stop on the side of 
the case so that the needle can be held at rest. Give sketch. 

11. Upon testing a bar magnet with iron filings it is found to attract 
filings at the centre and also at each end. How do you account for 
this ? Give sketch to illustrate your answer. 

12. A watch is placed in a small pocket-case, which looks like hard 
rubber, to prevent it from becoming magnetised. What is the case 
made of, and what is the principle involved ? 

13. What are consequent poles ? Illustrate your answer by a 
sketch. 

14. A bar magnet repels a poised needle 45 degrees, at a distance 
of 4 inches. An incandescent lamp bulb, containing a vacuum is in- 
terposed between needle and magnet. Will the deflection be greater 
or less ? Why ? 

15. Give several examples of substances that could be interposed in 
question 14 without disturbing the needle. What are these sub- 
stances called ? 

16. A piece of hard steel is interposed in question 15. How is the 
deflection affected? Give sketch showing the direction of the lines 
of force between the needle, the steel, and the bar magnet. 

17. What is a magnetic screen, and for what purpose is it used ? 

18. How would you diminish the earth's attractive force on a mag- 
netic needle ? 

19. A horseshoe magnet is laid flat in a suspended fibre stirrup. 
What position will it take up when allowed to come to rest in the 
earth's field? 

20. Why is it necessary to harden a piece of steel before it is 
magnetised ? 

21. What is residual magnetism, and what is its particular value? 

22. State several ways in which you could destroy, or materially 
weaken the strength of a good permanent magnet. Give reasons for 
your answer. 

23. What care should be exercised in handling instruments contain- 
ing permanent magnets ? 

24. A piece of iron is suspended in a stirrup and attracted by the 
poles of a horseshoe magnet located some little distance underneath 
it, The N-pole of the bar magnet is approached to one end of the 
piece of iron, and it is repelled. State the condition of the bar at first 
and what occurred to cause the repulsion. Give sketches to illustrate 
the answer. 

25. What is your idea of the lifting power of magnets ? 



LESSON VI. 

MAGNETIC CIRCUITS. 

Magnetic Circuits — Magnetic Bodies Free to Move — Test for the Dis- 
tribution of Magnetism — Testing Distribution by a Needle's 
Oscillation — Pole Pieces, Armatures, and Keepers — Questions. 

42. Magnetic Circuits. — A simple magnetic circuit is one 
composed wholly of a magnetic substance throughout its 
entire length, and having a uniform cross-sectional area, as, for 
example, an iron ring, Fig. 178. In a compound magnetic 
circuit the lines of force pass consecutively through several 
magnetic or non-magnetic substances, as, for example, an iron 
ring with a section removed, Fig. 178. The lines would 
then pass from the iron through an air-gap back to the iron 
again. If the ring were cut into quarters, four air-gaps would 
be introduced into the magnetic circuit. A closed magnetic 
circuit is one affording a complete magnetic path for the lines 
of force through magnetic substances, for example, an electro- 
magnet core, the keeper of which is wrought iron, the limbs 
of steel, and the yoke of cast iron. See ^| 195. 

43. Magnetic Bodies Free to Move. — If a graphical 
magnetic field be made of a bar magnet and a piece of iron 
lying in the field, it will be noted that the magnet's field is 
distorted, and many of the lines pass through the piece of 
iron. Magnetic lines of force always choose the path of least 
resistance. If the piece of iron is arranged free to move in the 
field, it will turn and take up such a position as to accommo- 
date through itself the greatest number of lines of force. If 
instead of being a magnetic body it is a magnet, it will move, 
under the influence of the magnetic field in which it is placed, 
not only so as to accommodate through itself the lines of force 
of the field, but also in a particular direction, so that its lines 
will be in the same direction as those of the field. Thus, 
N -lines merge from one point and enter as S-lines at another 
point (Figs. 47 and 48 will serve to illustrate this principle). 
The fundamental principle in many forms of electrical meas- 

36 




: wrm 



MAGNETIC CIRCUITS. 37 

uring instruments and electro-mechanical devices is that a 
magnetic body, free to move under the influence of a magnetic 
field, tends to move, so as to accommodate through itself, the 
greatest number of lines of force of the field. If the movable body 
is a magnet it moves in a particular direction so that its own 
internal magnetic lines will be in the same direction as those 
of the field in which it is placed. 

44. Test for the Distribution of Magnetism. — According 
to the molecular theory of magnetism, the relative strength 
of free magnetism along a bar magnet increases from zero at 
the centre until it reaches its maximum near the ends, or 
poles. To prove this, support a long bar magnet horizontally 
and apply a number of soft iron nails 
in chains to successive points on the 
supported magnet. No nails will at- 
tach themselves to the magnet at the 
neutral line, but a gradually increasing 
number may be suspended until the 
poles are reached, but beyond the poles 
not quite so many. See lower half of 
Fig. 49. In this figure the dotted ver- 
tical lines above the magnet have been 

drawn of such length as to graphically Fig. 49.— Testing Magnetic 

. , -i -i ; ■ , v • x £ e " Distribution by Tacks, 

represent the relative quantities ot tree 

magnetism at different points on the bar magnet, and the 
ends of these lines have been joined by a curve which rep- 
resents to the eye the relative amount of free magnetism at 
all points on the bar. 

45. Testing Distribution by a Needle's Oscillation.— A bar mag- 
net may be tested for free magnetism by causing a needle to oscillate 
at successive points near the magnet, from pole to pole. Support the 
bar magnet vertically, and hold the needle close to the magnet (al- 
ways at the same distance from the magnet for each position 
selected) ; deflect the needle from the position it takes up with refer- 
ence to the magnet, and then count how many vibrations forward 
and backward it makes in a given time (one-half minute), which will 
be the rate of oscillation of the needle. Find how many oscillations 
are made at other positions equidistant from the magnet in the 
same time. Move the needle away from the magnet, and ascer- 
tain how many oscillations it makes in the same time, when 
under the influence of the earth's magnetism alone. After making 
a number of tests, as at the positions shown in Fig. 50, square 
the number of oscillations for each position, and subtract from 
each value thus obtained, the square of the oscillations that the 
needle made in the earth's field. The resulting numbers will be a 



38 



PRACTICAL ELECTRICITY. 



-Pok- 



es"^- — 

4.8X7—- 
3SX— 



9 V 



series of values representing the quantities of free magnetism along 
the bar. These numbers may be plotted to scale on lines drawn at 
right angles to the magnet at points corresponding to the positions 

selected, as in Fig. 50, 
and by connecting all the 
points by a line, a graphi- 
cal representation of the 
free magnetism along a 
bar magnet is obtained. 
For example, suppose that 
a magnetic needle makes, 
four to-and-fro swings in 
one-half minute, under 
the influence of the earth's 
magnetism, and seven os- 
cillations in one-half min- 
ute, when near the pole 
of a magnet, then (7 2 — 4 2 ) 
equals (49—16) equals 83, 
so that 33 represents the 
length of the line to be 
drawn to any convenient 
scale at this position of 
the needle. The follow- 
ing table records the data 
of a needle oscillating test, and Fig. 50 illustrates the plotting of the 
curve, and also shows the number of oscillations obtained at each 
position. At the neutral line it will be noted that the oscillations are 
four, the same number as obtained in the earth's field above : 



&~9 




pote- 



Fig. 50. — Testing Magnetic Distribution 
by the Needle. 



Table I— Oscillation Test. 



Oscillations. 


Oscillations 
squared. 


Oscillations squared 
minus Earth's Oscilla- 
tions squared. 


Relative Quantities 
of Free Magnetism. 


At centre 4 
" 5 
" 6 

" 8 

" 9 

At pole 10 

" 9.8 


16 
25 
36 
49 
64 
81 
100 
96 


16 — 16 
25 — 16 
36 — 16 
49 — 16 
64 — 16 
81 — 16 
100 — 16 
96 — 16 




9 

20 

33 

48 
65 
84 
80 



46. Pole Pieces, Armatures, and Keepers. — To concen- 
trate and direct the magnetic lines of force, which extend in 
all directions from the poles of a magnet, pole pieces made of 
iron in a variety of shapes are fastened to the magnet's poles. 



MAGNETIC CIRCUITS. 



39 



Pole pieces of soft iron, Fig. 51, are attached to the ends of 
the limbs of the magnet and serve to direct or concentrate 
most of the lines of force between them. In a dynamo these 
magnetic lines are cut by the rotation of a bundle of wires 
wrapped upon an iron core, constituting what is known as 



r\ 



(HOLD 

Fig. 51. — Permanent Magnet with 

Iron Pole Pieces (P) and 

Armature (A). 




Fig. 52.— Electromagnet with 
Armature (A). 



the armature, represented in Fig. 51 by A. An armature is 
a magnetic body placed between or near, but not touching, 
the poles of a magnet, and is free to be rotated or moved to 
and from the poles. A different type of armature from that 
used in a dynamo is illustrated in Figs. 52 and 53, where a 
piece of iron is attracted to the poles against 
the action of a spring. A keeper is a piece of 
soft iron placed across the poles to connect 
them. Fig. 54. Its function is to provide 
a complete short circuit, or closed path, for 
the magnetic lines between two unlike poles. 



n s 



$ 




Fig. 53.— Polarized 
Armature. 



Fig. 54. — Horseshoe 
Magnet with Keeper. 



The magnetism induced in the keeper reacts on the magnet, 
and not only helps to maintain the strength of the magnet, 
but also serves to augment it. A magnet deprived of its 
keeper gradually loses its magnetism. Steel is much more 
readily demagnetised than magnetised, so that magnets re- 
quire careful handling when in use and should be provided 
with keepers when put away. 



40 PRACTICAL ELECTRICITY. 

QUESTIONS. 

1. A horseshoe magnet attracts a compass needle. A piece of soft 
iron is placed across the poles of the magnet and the needle returns 
to nearly its natural position. Explain this. 

2. Explain and illustrate by sketches the difference between a 
simple, a compound magnetic circuit, and a closed magnetic circuit. 

3. How would you magnetise a steel key-ring so that it would 
have two poles ? 

4. A steel sphere is attracted by a bar magnet but does not roll to- 
ward it. When a soft iron sphere is substituted and placed at the 
same distance from the same magnet, the attractive force causes it to 
roll to the magnet. How do you account for this, since the same 
magnet was used in both cases? 

5. How would you put away three bar magnets without keepers 
so as to preserve their magnetism ? 

6. Magnetisation always precedes attraction of an unmagnetised 
body for one that is magnetised. How would you prove this statement 
in the case of a piece of soft iron attracted by a magnet. 

7. A short rod of unmagnetised soft iron is suspended in a stirrup, 
and placed along the equator of a bar magnet a little distance from it, 
What position will it take up with reference to the magnet ? Give 
sketch. 

8. A short piece of magnetised steel is substituted for the piece of 
iron in question 7. What position will it take up ? Give sketch. 

9. Give a concise statement as to the movement of a magnetic 
body (when free to move), if placed in a magnetic field. 

10. A piece of iron is fastened at right angles to a poised magnetic 
needle at the neutral point so that it extends over each side equally. 
What effect will it have on the position the needle will take up in the 
earth's field? Give sketch. 

11. A steel magnet is substituted for the piece of iron in question 
10. What position will the combination now take up ? Give sketch. 

12. The following number of oscillations were recorded in a test for 
distribution of free magnetism of a bar magnet. At the ends 10, then 
12, 10, 8, 6, and at the centre 4. The needle oscillated four times in 
the same length of time when under the influence of the earth's field 
alone. Find the relative quantities of free magnetism for each posi- 
tion. Plot the points to scale and draw a curve to illustrate the mag- 
netic distribution. 

13. Sketch the positions a test needle would occupy when used to 
explore the field of a horseshoe magnet. 

14. How would you magnetise a horseshoe magnet with two bar 
magnets, so that both ends would have a N-pole and the S-pole 
located where the neutral point generally is located? Give sketch. 

] 5. The pole of a bar magnet projects over the edge of the table and 
a piece of iron is attracted to it. Another magnet is brought near the 
projecting pole and the iron drops off. How do you account for this ? 
Give sketch. 

16. You are given a compass needle, and two exactly similar bars, 
one of iron, the other of steel. How would you distinguish the iron 
from the steel bar? Give sketch. 



LESSON VII. 

EARTH'S MAGNETISM. 

The Earth's Magnetism— Polarity of the Earth— The Earth's Mag- 
netic Field and Equator — Graphical Field of the Earth's Magnet- 
ism — The Magnetic Meridian-Declination— Inclination or Mag- 
netic Dip — Magnetic Maps or Charts — The Mariner's Compass — 
Magnetisation by the Inductive Effect of the Earth's Field— The 
Earth's Field Directive, Not Translative — Neutralizing the 
Earth's Attractive Force for a Needle — Astatic Needles — 
Questions. 

47. The Earth's Magnetism. — Lay a bar magnet flat on 
the table and hold over it a freely suspended magnetic needle 
at different positions from pole to pole, as in Fig. 49. At the 
N-pole the needle will be vertical, with its S-pole pointing 
down ; when opposite the neutral point, or equator, it will be 
horizontal ; when over the S-pole it will be vertical, with its 
N-pole pointing downward. A freely suspended needle car- 
ried around the earth from its N to its S -geographical pole 
will take up similar positions. At a point near the N-geo- 
graphical pole the needle becomes vertical, with its N-pole 
pointing down ; at the earth's equator it is horizontal, and 
near the S-geographical pole it again becomes vertical with 
its S-pole pointing down. The earth may thus be regarded 
as a huge magnet, with two magnetic poles. Suppose a hole 
to be drilled through the earth's centre from pole to pole, 
making an angle of about 20 degrees with its axis, and a bar 
magnet of somewhat less length than the diameter of the earth 
to be inserted with its N-pole pointing toward the S-geo- 
graphical pole, the resulting distribution of magnetism would 
be similar to the earth's magnetism. 

48. Polarity of the Earth. — We have called the N -seek- 
ing, or marked pole of a magnet, its N-pole, and, as unlike 
poles attract each other, it will naturally be inferred that the 
nature of the magnetism near the earth's N-geographical pole 
is S-magnetism. The true S-magnetic pole is located in the 
northern hemisphere, while the true N-magnetic pole is 
in the southern hemisphere, Fig. 56. The earth's true mag- 

41 



42 



PRACTICAL ELECTRICITY. 






netic S-pole is not coincident with its N -geographical pole, 
but about 1400 miles west of it. The N -magnetic polar 
region has not been definitely located. 

49. The Earth's Magnetic Field and Equator.— The 
geographical equator is an imaginary belt passing around the 
earth midway between its poles. So also, the magnetic 
equator is an imaginary line encircling the earth midway 

/ ^ between its magnetic 

//$&..*&- ^ poles (Fig. 56) ■ and 

connecting all those 
points which show no 
magnetic dip, or where 
the needle was found 
to be horizontal (see 
% 52). This mag- 
netic equator is some- 
what irregular in form, 
owing to the irregular 
distribution of the 
e a r t h' s magnetism. 
The lines of force of 
the earth's magnetic 
field may be consid- 
ered to emanate from 
the true N -magnetic 
pole in the southern 
hemisphere, and curve around over the surface of the earth, 
entering again at the true S-pole. The lines of force act on 
a freely suspended magnet in such a manner, that it turns 
on its axis, until it lies as nearly as possible in the direction 
of the lines of force, according to the principle enunciated in 
II 43. 

50. Graphical Representation of the Earth's Mag- 
netic Field. — Magnetise a large steel sphere, such as is used 
in roller bearings, by placing it between the unlike poles of 
two bar electromagnets so that its diameter and the axis of 
the magnets form a straight line. When plunged into filings 
the poles are readily observed. Cut a hole, equal to the di- 
ameter of the ball, in a sheet of cardboard and place it over 
the sphere horizontally so that its plane passes through the 
axis of the sphere containing the poles. Make a graphical 
field by the aid of iron filings, as shown in Fig. 58, and you 




Fig. 56.- 



-The Earth's Magnetic Poles 
and Equator. 



EARTH'S MAGNETISM. 



43 




Fig. 58. — Field of a Magnetised 

Steel Sphere Representing 

Earth's Field. 



have a typical representation of the magnetic lines of force 
surrounding the earth, and called the earth's field. 
51. The Magnetic Meridian — Declination.— Just as the 

geographical meridian is an im- 
aginary line, drawn on the earth's 
surface in a plane which passes 
through the geographical poles of 
the earth and a given place, so, 
also, the magnetic meridian may 
be regarded as an imaginary line 
drawn on the earth in a plane 
which passes through the mag- 
netic poles of the earth and a 
given place, or a line in the verti- 
cal plane containing the axis of 
a magnetic compass needle at any 
given place. At most places the 
geographical and magnetic meri- 
dians differ, and the angle be- 
tween them is known as the angle 
of declination of any given place. 
It indicates just how far away from the 
true geographical north the compass needle "Eartk'*f$\poi* 
points. This angle of declination is very jv\IZfc\ 

slowly, but constantly changing. In New / f j j \\ 
York city in 1900, the declination was 9° / / ; j 
12' W., which means that when the com- ( j J *_ \\ 
pass needle comes to rest at this place the ; ,' / 
true geographical north will be 9° 12' to j j j 
the east of the direction the needle points. \ \ \ 

Suppose a person to be located at point \ \ 
A, Fig. 56, the direction of true north is \ \ 
along the line AC, while the compass \\ 
needle at position A points along line AB. \> 

The angle between these lines is the angle Earth-A ' 
of declination. In Columbus, Ohio, and 
Charleston, S. C, in 1900, the declination ^^^-T^Polarity 
was zero ; that is, the true N-pole was just Magnet. 

in line with the magnetic pole at these 
points, or the two meridians coincided. Moving west from 
point A, Fig. 56, the declination decreases until a locality is 
found in central Asia where the meridians again coincide. 



I 4 



44 PRACTICAL ELECTRICITY. 

Places in the Atlantic Ocean, Europe, and Africa, between these 
lines of no declination, would have a declination west of the 
true N, while at places on the other side of the globe between 
these lines the needle would point east of the true north. In 
steering ships at sea by the compass, references are made to a 
chart, giving the localities corresponding to the different 
values of the declination of the needle. 

52. Inclination or Magnetic Dip.— If a long knitting 
needle be carefully balanced and suspended by a silk thread, 
it will' assume a horizontal position. When magnetised its 
N-end will point downward, or dip toward the earth's mag- 
netic S-pole. This needle be- 
ing free to move in all direc- 
tions, takes up a position along 
the lines of force of the earth's 
field. The angle which the 
needle makes with the horizon- 
tal is termed the angle of dip. 
The dip needle (see % 20) 
is horizontal at the magnetic 
equator, and the angle of dip 

Fig. 6i.-Angle of Dip. increases as you go toward 

either pole, the needle being- 
vertical at the poles. At New York city in 1900, the 
dip was 70° 6' N. , which means that the knitting needle, 
or dip needle, as shown in Fig. 19, will take up a position 
with its axis at 70° 6' with the horizontal plane with its N- 
end pointing downward, Fig 61. 

53. Magnetic Maps or Charts. — Magnetic maps are pre- 
pared, on which the places of equal magnetic dip are con- 
nected by lines which run similar to the parallels of latitude, 
but quite irregular, and are called isoclmic lines. Similarly, 
lines connecting places of equal magnetic declination are 
called isogonic lines. They correspond with the meridians 
of longitude, but are also irregular. Such maps are prepared 
from time to time by the United States Geodetic Survey, and 
are used in determining localities, especially in connection 
with the mariner's compass on board ships. 

54. The Mariner's Compass. — In small pocket com- 
passes the magnetic needle is poised on a jewel bearing, and 
above a graduated scale, fastened to, or engraved on the con- 
taining box. In using this compass, it is first necessary to 




EARTH'S MAGNETISM. 



45 




Mariner's Compass. 



permit the needle to come to rest pointing N and S, and then 
gently twist the box around until the point marked N on the 
scale, is directly under the 
N-pole of the needle. The 
true geographical north 
will then be so many de- 
grees east, or west of the 
position the needle assumes 
when pointing to the N, or 
marked position, on the 
scale. See ^[51. In the 
mariner's compass the 
needle is fastened to the 
underside of the cardboard 
scale, and needle and scale 
swing around together, the 
N-point on the scale 
always pointing to the 
north. When it is desired to steer in any particular course, 
as northwest, the ship's helm is turned till the northwest 
on the movable dial is opposite a fixed vertical black 
line (termed the "lubber line ") which is drawn on the in- 
side of the bowl, J4, Fig. 62, in line with the direction of 
the ship's motion. The compass box is supported on gimbal 
bearings, so that no matter how much the ship may roll or 
lurch the card will always be level. The construction and 
method of support are shown in the sectional view, Fig. 62, 
and the plan in Fig. 63. Many precautions have to be taken 
in adjusting a ship's compass, to compensate for several 
errors likely to arise, caused by the influence on the needle 
of the hull, or the cargo, or electric light wires in the 
vicinity, etc. 

55. Magnetisation by the Inductive Effect of the 
Earth's Field. — Procure a soft iron bar about 14 inches 
long, test it for polarity, and then hold it in one hand in the 
magnetic meridian, with one end pointing or dipping down- 
ward at an angle of about 70 degrees to the horizontal, Fig. 
64. Strike the bar several hard blows with a hammer, and 
then test for polarity. The lower end will be found to possess 
a N -seeking pole, and the upper end a S-seeking pole. 
Reverse the bar, after first demagnetising it by blows while 
held in an east and west direction, and the lower end is again 



46 



PRACTICAL ELECTRICITY. 



magnetised and becomes N-seeking. The earth's field has 
induced poles in the bar by induction, the hammer blow 
simply assisting the molecules to turn around according to 

the molecular theory. In a 
like manner tests made with 
a compass needle on iron and 
steel girders in buildings 
under construction, will show 
that the bodies have been 
magnetised by the inductive 
action of the earth's field. 
It seems probable that the 
natural magnet, or lodestone, 
is due to the earth's magnetic 
inductive action. 

56. The Earth's Field 
Directive, Not Translative. 
— Float a bar magnet on a 
cork in a basin of water. 
The bar takes up a N and 




Fig. 63. 



■Plan of Compass Card and 
Bowls. 



Index to Figs. 62 and 63. 

CB represents Compass Bowl 

and Card. 
JxJ 2 represents Compass Bowl 

Journals. 
GR represents Gimbal Ring. 
J 3 J 4 represents Gimbal Ring 

Journals. 
BB represents Binnacle Bowl. 
I represents Lubber Line 

(Fig. 62.) 

S-position, due to the 

earth's field, but is not 

attracted toward the side VSR&SMBjfflim 

of the basin nearest to the ^ 

earth's magnetic S-pole, 

as might be expected, we 

being so much nearer the 

south than the north 

magnetic pole. The poles Fi ' g# 64 ._ M agnetisation by the Earth's Field. 

of the earth are so far 

away that the short distance between the two poles of the bar 
ceases to be of any account, when compared with the distance 
of these poles from the earth's poles. The forces of attraction 




Test- needle. 



EARTH'S MAGNETISM. 



47 




and repulsion on one pole may, therefore, be considered equal 
and opposite, so that the bar is simj:>ly directed, and there 
is no motion of translation. The distance through which 
the earth's magnetic pole at- 
tracts the N-pole of a mag- 
netic needle is less than the 
distance through which the 
S-pole of the needle is re- 
pelled by the earth's S-pole. 
This difference in the dis- 
tances between the two poles 
of the earth is so small (equal 
to the length of the magnet) 
that the force of attraction is 
practically no greater than that of repulsion. The needle, 
therefore, turns in the direction of the two forces, but there 
is no motion of translation. If the pole of another magnet 
be approached to the floating magnet, Fig. 65, at such a dis- 
tance that the length of this magnet is considerable, as com- 
pared with the distance between the two magnets, then the 
floating needle will be both directed and attracted. 

57. Neutralizing the Earth's Attractive Force for a 
Needle. — Hold above, and parallel to a compass needle, a 
bar magnet with its N-pole pointing in the same direction as 



Fig. 65.— The Earth's Force not 
Translative. 



E 



1 



D 



n-« 



X 



Fig. 66. — Neutralizing the Earth's Attractive Force for a Needle. 



T-»n 



the needle's N-pole, Fig. 66. If the height of the bar is 
considerable, the needle is not appreciably affected. Slowly 
lower the magnet, and a point will be found where the needle 
will be observed to waver. If the magnet be fixed at this 



i 



R L 


IN 






A 


Ml 


Is 



48 PRACTICAL ELECTRICITY. 

position the needle will stand in any position given to it, 
showing that the earth's directive attracting force has been 
neutralized. If the bar magnet is further lowered, the needle 

swings around and takes 
up the position shown in 
the right hand diagram of 
Fig. 66. A bar magnet 
used to neutralize the 
earth's field in this man- 
ner is used in some gal- 
vanometers. (See Fig. 
163.) 

Fig. 67.— Astatic Needle. 58. Astatic Needles. 

— If two similar bar mag- 
nets, equally magnetised, be fixed to a rigid support, one above 
the other, with unlike poles at the same end, Fig. 67, the 
system will be independent of the earth's magnetism, and 
will come to rest in any desired position. When two needles 
are so arranged they form what is called an astatic needle. 
Astatic means without polarity, and such needles are used 
in very sensitive galvanometers, Fig. 167. 

QUESTIONS. 

1. Explain your idea of the earth's magnetism. Make sketch. 

2. What is meant by the polarity of the earth's magnetism? 

3. How do you account for the fact that the N-pole of a magnet 
always points N, since like poles repel each other? 

4. Sketch the position a test needle will take up if used to explore 
the earth's field. 

5. What is the earth's magnetic equator? Give sketch. 

6. What do you understand by the magnetic meridian? Give 
sketch. 

7. Describe and illustrate what is meant by magnetic declination. 

8. A long knitting needle is careiuily balanced so that when sus- 
pended in an east and west position it remains horizontal, but when 
pointing N and S it acts as if one end had been weighted. How do 
you account for this ? Give sketch. 

9. Of what value are magnetic charts and how are they con- 
structed ? Give sketch. 

10. What do you understand by an inclination of 70° 6' N ? 

11. How does the construction of a mariner's compass used on 
board ship differ from a little magnetic test needle ? 

12. A soft iron bolt is held in the earth's magnetic meridian at the 
proper angle of inclination, with the head pointing downward and 
struck several blows with a hammer. The head is then presented tq 
the N-pole of a compass needle. How does it affect the needle ? 



LESSON VIII. 

VOLTAIC ELECTRICITY. 

Electricity — Electrical Effects — Generation of Electric Currents by 
Chemical Means— A Current of Electricity — Simple Voltaic Cell 
— Volta's Pile — The Circuit— Conductors and Insulators — Direc- 
tion of the Current— Poles or Electrodes and Plates — Detector 
Galvanometer— Potential and Electromotive Force — Chemical 
Action in a Voltaic Cell — Why the Hydrogen Appears at the 
Copper Plate — Polarization— Table H-Polarization Test— On 
What the Electromotive Force of a Cell Depends— Table III- 
The Electro-chemical Series — Local Action — Amalgamation — 
Questions. 

59. Electricity. — The word electricity has been applied 
to an invisible agent which makes itself known to us by 
various properties, commonly termed electrical effects, or man- 
ifestations. While the exact nature or constitution of elec- 
tricity is not known, the laws governing electrical phenomena 
are clearly understood and defined, just as the laws of gravi- 
tation are known, although we cannot define the constitution 
of gravity. Electricity is neither matter no? energy, yet it can 
be associated with matter, and energy can be spent in moving 
it. Its commercial advantage is due to the fact that energy 
can be spent in generating electrical force at one point, which 
can be transmitted and utilized at some distant point. Elec- 
tricity can neither be created nor destroyed, but it can be 
transformed in its relations to matter and energy, and be 
moved from place to place. While it is neither a gas nor a 
liquid, its behavior sometimes is analogous to that of a fluid, 
so that it is said to floiv through, or around a wire. This 
expression of "flowing," however, should be regarded as a 
convenient expression for the phenomena involved rather 
than an accurate account of what really transpires when a 
wire possesses electrical properties. 

60. Electrical Effects. — The manifestations produced by 
electricity may be divided into four distinct classifications 
for studying the subject. First, electricity ivhen at rest is known 
as statical electricity and the bodies electrified are said to be 
statically charged; the term electrostatics applies to this subject, 

49 



50 PRACTICAL ELECTRICITY. 

Second, electricity in motion differs from statical electricity and 
is treated as a current of electricity. Third, electricity in 
motion produces magnetism which has been termed electro- 
magnetism. Fourth, when electricity is vibrated very rapidly 
it produces a fourth state, known as electrical waves. All 
these phenomena are very intimately associated with each 
other, and are due to the one invisible agent, electricity. In 
this book we will limit the study to currents of electricity and 
electromagnetism, which form the basis of a great many prac- 
tical electrical applications. 

61. Generation of Electric Currents by Chemical 
Means. — 

Experiment 1 : Fill a tumbler two-thirds full of dilute sulphuric 
acid (one part acid to 20 parts water) and partially immerse in the 
same a strip of sheet zinc, say one inch wide by five inches long. 
Bubbles of gas immediately collect on the zinc, and then detaching 
themselves, rise to the surface of the liquid, being rapidly replaced 
by other bubbles as the action continues. - These bubbles of gas are 
hydrogen (one of the gases of which water is composed) and when 
collected, by displacing water in an inverted test tube held over 
them, this gas may be ignited, and will burn with a pale bluish flame. 
If the zinc remains in the acid for some time it 
wastes away or is dissolved in the liquid. 

Exp. 2 : Place a strip of copper, of about the 
same dimensions, partially in the acid as before. 
No bubbles of gas are seen rising from the copper. 
If this metal is allowed to remain for some time it 
will not apparently be acted upon by the acid. 

Exp. 3 : Place the strips of copper and zinc in the 

tumbler of acid, not permitting them to touch each 

other, inside or out. Hydrogen gas continues to 

rise from the zinc as before, but there is no action 

Fig. 69.— Copper on tne copper plate. Bring the outer extremities 

and Zinc in Acidu- of the copper and zinc strips into contact, Fig. 69, 

lated Water. and torrents of bubbles are noiu seen to rise from the 

copper strip, in addition to the bubbles rising from 

the zinc strip. If collected, the gas evolved from the copper proves to 

be hydrogen, the same as that rising from the zinc. If the action is 

permitted to continue for some time, upon examination the zinc is 

found to have wasted away, while the copper remains unchanged. 

Break the external contact between the plates and the action at the 

copper instantly ceases, but the zinc wastes away as before. 

Exp. 4 : Remove the zinc strip from the liquid, and while it is 
still wet with the acid rub over its surface a little mercury. Upon 
being replaced in the solution the acid does not attack it. Repeat 
Exp. 3 with this " amalgamated zinc" (see If 76), and note that 
now bubbles rise only from the copper plate, when the ends of the 
two strips are brought together, and that none rise from the zinc 
plate, but that it is still the zinc plate which wastes away. 




VOLTAIC ELECTRICITY. 



51 



Exp. 5 : Connect wires of any metal to the copper and zinc plates, 
being sure that you have bright metallic contacts. Bring the ex- 
tremities of these two wires together after they have been brightened 
and hydrogen gas is seen to rise from the copper plate as before, while 
there is no action at the zinc. 

When the wires are separated the action ceases, but com- 
mences again as soon as connection is made. Interpose 
between the two connecting wires pieces of glass, mica, rubber, 
paper, wood, porcelain, etc., or connect the two plates by a 
bridge made of any of these materials, no action appears at 
either plate. 

It thus requires a connection between the two plates to 
cause chemical action, and this connection must be of a 
particular kind. It would seem that the plates exert an in- 
fluence upon each other through the connecting wire. W T e 
will now ascertain whether 
the connecting wire pos- 
sesses any extraordinary 
qualities when thus con- 
nected with these dissim- 
ilar plates. 

Exp. 6 : Set up a poised 
magnetic needle pointing N 
and S. Bring above and 
parallel to it a portion of the 
connecting wire used in the 
last experiments (as in Fig. 
70). 

Fig. 70. — Deflection of the Magnetic Xeedle. 

\\ hen the ends of the 
wires are brought together the needle immediately turns 
upon its axis at right angles, or nearly so, to the wire, after a 
few vibrations, and remains in this position until the con- 
nection is broken, when it assumes its normal position. The 
deviation of the needle from its original position is termed 
the deflection of the needle. Xote that chemical action con- 
tinued in the tumbler as long as the needle was deflected, 
and at the expense of the zinc rod. 

Exp. 7 With the wire arranged as in Exp. 6, interpose pieces of 
tin, steel, copper, iron, lead, gold, brass, aluminum, etc., between 
the connecting wires, and the needle is deflected as before. AVhen 
pieces of paper, glass, wood, mica, etc., are interposed, however, 
there is no deflection of the needle, which again proves the necessity 
of a suitable connector between the copper and zinc plates. 

Exp. 8 : Test an iron rod by iron filings for magnetism. It does 




52 PRACTICAL ELECTRICITY. 

not attract them. Wind a few turns of cotton-covered wire around 
the iron rod and plunge it into the filings, after first connecting the 
ends of the wires to the two plates in the tumbler. Filings are now 
attracted to the iron core, but drop off when the connection to the 
plates is broken. This then, is a temporary magnet, produced by 
the magnetic properties possessed by the wire. 

62. A Current of Electricity. — From. the foregoing ex- 
periments it appears, that when zinc and copper are immersed 
in an acid solution and connected .by a wire, the wire pos- 
sesses unusual magnetic properties. The cause of this magnetic 
effect, and other effects associated with it to be noted later on, 
is attributed to electricity, and the property possessed by the 
wire said to be due to a transference of electricity from one 
plate to the other, the wire acting as a conducting medium. 
When we speak of a current " flowing through the wire from 
plate to plate," it is simply a convenient expression used to 
describe the phenomena involved, although we do not know 
what actually transpires. 

An ebonite or glass rod is electrified when rubbed with 
flannel, silk, etc. , and possesses the power of attracting light 
bodies to it, and also of attracting or repelling another sim- 
ilarly electrified rod, according to the nature of its electrifica- 
tion. When the portion of a rod so electrified is touched by 
the hand, or other conductor, the electrification disappears 
and the body is said to be discharged. The two plates in the 
tumbler may be said to be electrified to different degrees of 
electrification, and when they are connected by a wire, the 
electrification discharges from the higher to the lower elec- 
trified plate. The action of the acid upon one plate more 
than the other, however, tends to keep the plates at different 
states of electrification and the successive discharges through 
the connecting wire become so intensely rapid that they form 
practically a continuous current of electricity. 

63. Simple Voltaic Cell. — When two dissimilar metals 
are partially immersed in acid solution, which is capable of 
acting chemically upon one of them more than upon the 
other, when they are connected by a wire, the combination 
constitutes a voltaic cell. The name voltaic is derived from 
an Italian physicist, Volta, who first discovered the cell in 
1800. It is sometimes called a galvanic cell, after Volta's 
contemporary, Galvani. Correctly speaking, the word battery 
a])plies to a number of such cells connected together, though 



VOLTAIC ELECTRICITY. 



53 



the name is commonly applied to a single cell. The solution 
in which the metals are immersed is called the electrolyte, or 
exciting fluid, or excitant. 

64. Volta's Pile. — Volta's pile, which is the parent of all 
batteries, consists of a number of discs of copper (C) and 
zinc (Z), Fig. 71, with a cloth or blotting paper (W) moistened 
with salt water and placed between them. When the end 
discs are connected by wires brought into contact, the same 
phenomena occur as already described with the Volta cell. 




/^^^pS 




Volta Pile. 



Fig. 71. 



Connections of Volta Pile. 



Volta soon found that better results were obtained by using 
the two metals immersed in an acid solution, hence our 
simple voltaic cell. 

Fig. 71 also illustrates a Volta pile made for experimen- 
tal purposes. It is equivalent to a number of Volta cells 
with the zinc of one cell connected to the copper of the next 
one, and so on. 

65. The Circuit. — Considering again our simple voltaic 
cell, Fig. 70, the term circuit is applied to the entire path 
through which the transference of energy takes place, or the 
current of electricity is supposed to flow, and the wire join- 
ing the plates is called the conductor. The circuit then con- 
sists of not only the conductor between the plates outside of 
the cell, but the liquid conductor between the plates inside 
of the cell ; hence we speak of the internal circuit and the 



54 



PRACTICAL ELECTRICITY. 



external circuit. The complete circuit includes the conducting 
wire, the two plates which act as conductors, and the liquid 
between them. Bringing the two extremities of the wires 
into contact is called making, or closing the circuit, and their 
separation again, opening, or breaking the circuit. 

66. Conductors and Insulators. — The substances which 
when interposed between the terminal wires of a voltaic cell 
do not interfere with the deflection of the magnetic needle 
(as the metals), are known as conductors of electricity, be- 
cause they allow the current to flow through them, while 
other substances so interposed, as glass, wood, mica, etc., 
interfere with the action in the cell and upon the needle, and 
are therefore called insulators. A classified list of conductors 
and insulators is given in ^| 125. 

67. Direction of the Current. — 

Exp. 9 : Place the conducting wire of a voltaic cell over and par- 
allel with a magnetic needle when it ia pointing N and S, Fig. 72. 

Close the circuit 
and note whether 
the N-pole of the 
needle points east 
or west when the 
current is flow- 
ing. Say it is de- 
fleeted to the 
east. Now re- 
verse the wire 
connections at 
the battery plates 
(that is, connect 
the end of wire 

which was attached to the zinc to the copper, and vice versa), the 
N-pole of the needle now points west if the wire is held as before. 

This experiment indicates that electricity exists in part, as 
a magnetic force around a wire, and on account of the be- 
havior of the needle, that this force has direction. For this 
reason electricians have agreed to assume that the electricity 
flows from the copper terminal to the zinc terminal through the 
conducting wire, and from the zinc plate to the copper plate 
through the solution. 

68. Poles or Electrodes and Plates.— The copper plate is 
called the negative plate or element, and the zinc plate the 
positive plate or element, while the external end of the copper 
plate or any wire connected thereto is called the positive pole or 
electrode (no connection whatever with magnetic pole), and 





Fig. 72. — Direction of the Current. 



VOLTAIC ELECTRICITY. 



55 



POSJTJVE 
POLE OB 
ELECTRODE 



tf£Z&TSVE 
PLATE 




the external end of the zinc plate, or wire connected thereto, 
the negative pole or electrode, Fig. 73. If we bring the -f- 
(plus sign for the positive) and — (minus sign for negative) 
wire from a cell together, making the circuit, the current 

passes from the + (copper) 
to the — (zinc) terminal 
across the junction, and also 
from the -f- plate (zinc) to 
the — plate (copper) through 
the cell. In any electro- 
generative device that pole is 

ELECTRODE to • -, -, ... t i' i 

considered positive from which 
the current flows, and that pole 
negative to which the current 
Hows. As Zn, stands for zinc, 
and negative begins with the 
letter N, this may aid in re- 
membering the terminals or 
poles. In any cell the posi- 
tive plate (generally zinc) is 
the one most acted upon, the 
current being supposed to 
start at the surface of this 
plate, travel through the solution to the copper plate, and 
from the copper terminal to the zinc terminal through the 
external circuit. 
69. Detector Galvanometer. — 

Exp. 10 : From Exp. 9 it was shown that if a current passes over a 
needle it is deflected to the east or west, according to the direction of 
the current. The student 
should now prove that the 
needle is deflected oppos- 
itely if the wire be held 
underneath, but parallel 
to it, according to the di- 
rection of current in the 
wire. Note also that for 
the same direction of cur- 
rent underneath the needle 

as ahove it, the deflection is opposite to what it previously was. Now 
bend the wire around the needle, at rest, parallel to it, so that the cur- 
rent flows over the needle and under the needle in opposite directions. 
The deflection is now in the same direction, and greater than before. 
Make several convolutions and the deflection is still increased, Fig. 
74. A few turns of wire wrapped around a pocket compass, parallel 



Fig. 73.— Nomenclature of a Voltaic 
Cell. 




Fig. 74. — Simple Detector Galvanometer. 



56 PRACTICAL ELECTRICITY. 

to the needle when it is pointing N. and S., constitutes a simple form 
of detector galvanometer, and when inserted in a battery circuit will 
indicate by the deflection of the needle that a current is flowing. 
Various types of galvanometers are described in Lesson XVI. 

70. Potential and Electromotive Force.— Suppose two 
vessels partially filled with w r ater are connected by a pipe 
and placed on a table at the same level. The connecting 
pipe is full of water, yet there is no current of water flowing 
through the pipe because the pressure at each end is the same. 
When one vessel, A, Fig. 75, is raised above the other, B, 

then there is a difference in pressure 

TC r ^ between the two ends of the pipe, 

wS| (Wjv and a current of water flows from 

i|f the higher to the lower level, due 

H \3L-<<v^^ to this difference of pressure (or 

I ^^^^ head) between the two points. It 

^^>Y is not necessary to know the 
4^ <CJi^ ne ight of vessel A or B above the 

IB m\ Hf sea l eve l> DU t the height or head 
W/M (H) between the two vessels. 
Similarly, if two points on a 

Fig. 75.— Water Analogy for PnTvnPT . kflr arp plpvnfpd in +Vip 

Potential Difference. copper Dai are elevated to the 

same temperature there is no 
transference of heat from one point to the other. If, however, 
one point is at a higher temperature than the other there is 
then a difference in temperature between the points and a 
transference of heat from the point of higher to the point of 
lower temperature. 

The w r ord potential as used in an electric sense is analogous 
to pressure in gases, head in liquids, and temperature in heat. 
In the Volta cell then we have two bodies raised to different 
electrical potentials (see ^[ 62), and to the difference of 
potential between them is due the current flowing through 
the wire connecting the plates. The greater this difference 
of potential the greater the current, or effect of the current 
produced. 

Potential is the force which moves electricity through the 
circuit. The total force required to cause the current to flow 
through the entire circuit is called the Electromotive Force, 
whereas a difference of potential would exist between two 
points in a circuit, which would cause the current to flow 
just between these two points. Electromotive force (abbre- 



VOLTAIC ELECTRICITY. 57 

viated E. M. F. ) is the total difference of potential (abbre- 
viated P. D.) that is maintained in any circuit. 

Exp. 11 : Insert two similar pieces of copper or zinc in the acidu- 
lated tumbler of water and test for a current by a detector galvan- 
ometer. The needle is not deflected. The similar plates being both 
electrified to the same degree there is no difference of potential be- 
tween them, hence no current. This is analogous to the two vessels 
of water placed on a level. 

71. Chemical Action in a Voltaic Cell. — A continuous 
potential difference is maintained between the zinc and 
copper plates when they are connected chiefly by the action 
of the exciting liquid upon the zinc. The chemist symbol- 
izes sulphuric acid, H 2 S0 4 , meaning that it is composed of 
two parts hydrogen (H 2 ), one part sulphur (S), and four 
parts oxygen (0 4 ). The S0 4 part of the acid has a strong 
affinity for the zinc, and when the cell circuit is completed, 
attacks the zinc and forms zinc sulphate (ZnSOJ which is 
dissolved in the water, and may be reclaimed by filtering 
after considerable zinc has wasted away. For every portion 
of the S0 4 part of the sulphuric acid which unites with the 
zinc, two parts of hydrogen gas are liberated, which escape 
from the solution as already noted in the experiments. The 
zinc thus replaces the hydrogen in the acid, setting it free. 
The chemical action may be expressed as follows : 

Zn -f H 2 S0 4 = ZnS0 4 -f H 2 . 

Zinc and sulphuric acid produce zinc sulphate and hydrogen. 

Every time the circuit of a cell is completed, and as long- 
as it is completed, this chemical action takes place, the zinc 
gradually wasting away, also the power of the acid to attack 
the zinc gradually becoming exhausted. Thus the electrical 
energy is maintained in the external circuit to perforin use- 
ful work by the expenditure of so many pounds of zinc and 
acid inside the cell. The chemical energy contained in a 
lump of coal is converted into kinetic energy when burned 
under a steam boiler. Zinc might be similarly burned to 
produce steam, but its cost would be prohibitive, and for this 
reason batteries are not cheap generators of electricity for 
electric lighting and power purposes. In coal and zinc there 
is stored up chemical energy which may be expended by 
bringing together suitable substances and converted into heat 
and electrical energy, as is done when zinc is practically 
burned in a battery. 



58 



PRACTICAL ELECTRICITY 



72. Why the Hydrogen Appears at the Copper Plate. 

— As already stated, when zinc is immersed in sulphuric 
acid, hydrogen is liberated and rises in bubbles to the surface 
of the solution. In the voltaic cell it was noticed that the 
hydrogen bubbles rose from the copper, yet no bubbles were 
seen to pass through the solution. Many chemists believe 
that the instant an element is liberated from a compound (as 
the H 2 from the H 2 S0 4 ) it possesses unusual readiness to 
enter into combination with other molecules. At the instant 
the circuit is closed, Fig. 76, the S0 4 of molecule 1 unites 
with a molecule of zinc, setting free a molecule of hydrogen ; 
this instantly unites with the S0 4 of molecule 2, forming a 
new molecule of H 2 S0 4 and setting free the H 2 of molecule 2. 
This action continues until the last free molecule of H 2 
appears at the copper plate and rises to the surface. 

73. Polarization. 

Exp. 12 : Connect a Volta cell to a detector galvanometer wound 
with a few turns of wire and note the angle of deflection of the needle. 
Allow the current to flow for a while, and note that the deflection 

«..- w~.. Gafoanomtlcr 




.Ctyper _( J),nne- Sulphuric _T) 



Sulphate 



Fig. 76.— The Chemical Action in a Voltaic Cell when the Circuit is Closed. 
The molecules of dilute sulphuric acid are represented by the ovals. 

gradually falls and becomes much less than at first. Brush off the 
bubbles adhering to the hydrogen plate with a swab and the deflec- 
tion is increased, thus indicating a stronger current ; but it soon falls 
again when the copper plate becomes coated with the hydrogen gas. 

The copper plate coated with hydrogen becomes practi- 
cally a hydrogen plate. Now the effect of using a plate of 
hydrogen and zinc in a cell would be to set up a current from 
the hydrogen to the zinc inside the cell and from the zinc to 
the hydrogen outside of the cell. As this tendency acts against 



VOLTAIC ELECTRICITY. 59 

the direction of the ordinary copper to zinc current it weakens 
the current from the cell. When the cell becomes weakened 
in this manner by a coating of hydrogen bubbles on the nega- 
tive plate it is said to be polarized and the phenomenon called 
polarization. Polarization, then, is an evil, which, if properly 
overcome by arresting the bubbles in some manner, would 
permit the cell to give a strong current as long as any zinc 
remained to be acted upon. The attempt to prevent the 
polarization has given us the many varied types of cells now 
on the market. 

The following test made on a Leclanche cell, f 88, will illustrate 
the phenomenon of polarization. The cell was connected to a circuit 
of low resistance, and readings of a voltmeter, ]f 235, were taken 
at one-minute intervals for five minutes, in which the E. M. F. 
dropped from 1.41 to .63 volts. The cell was then allowed to stand on 
open circuit for five minutes, and one-minute readings taken, to note 
its recuperation. At the end of the fifth minute the former E. M. F. 
was not regained, but only 1.18 volts. One-half hour after the test, a 
measurement then made showed the original E. M. F. of 1.41 volts. 



Table II.- 


-Polarization Test. 




Discharge. 

minutes, 1.41 volts. 

1 " 1.03 " 

2 " .80 " 

3 " .70 " 

4 " .65 " 

5 " .63 " 


Recuperation. 

minutes, .63 volts 

1 " .87 " 

2 " .97 " 

3 " 1.06 " 

4 " 1.14 " 

5 < 1.18 " 



74. On What the Electromotive Force of a Cell De- 
pends. — If two similar plates of zinc are immersed in an 
acid solution, Exp. 11, and connected, there is a tendency 
to opposite currents, which neutralize each other; since 
there is no difference of potential between them, no current 
flows. The essential parts of any cell, then, are two dissimilar 
metals immersed in an acid solution, one of which is more readily 
acted upon by the acid than the other. The greater the difference 
in intensity of chemical action the greater the difference of 
potential, and the greater the current strength which depends 
upon the difference of potential. 

Other metals than copper and zinc may be used in cells, 
and as acids attack the different metals with varying intensi- 
ties of chemical action, some combinations will produce bet- 
ter results than others. For example, a cell composed of 
zinc and lead plates, immersed in dilute sulphuric acid, will 



60 PRACTICAL ELECTRICITY. 

not deflect a magnetic needle to so great an angle as a zinc- 
copper cell of the same size, because a higher difference of 
potential is set up between zinc and copper than between zinc 
and lead. 

The electromotive force of a cell is dependent also on the 
solution used to attack the zinc, so that the same battery 
plates immersed in different acids would indicate different 
potential differences, for the combination in each solution 
used. Using the same solution, however, this force is inde- 
pendent of the size of the plates, a small battery having the same 
'potential difference, or E. M. F. r as a large one of the same kind. 

In the following list of substances, known as the electro- 
chemical series, those most acted upon (electro-positive plates) 
by dilute sulphuric acid are placed at the left-hand of the 
list, while those least acted upon (negative plates) are at the 
right-hand end of the list. 

The arrangement would be different for other acids used. 

Table III.— The Electro-chemical Series. 

Direction of current through external circuit. 

< m 



Positive 



plates. g g • ^ & 

S3 m H h1 O 





a 






S-l 


q 


q 
o 


Negative 


> 


•i-i 

-1-3 

o3 




plates. 






o3 




be 


s 


O 





Direction of current through solution. 

The difference of potential in a lead-silver cell would be 
less than a lead-carbon cell, while an iron-carbon cell would 
be greater, and a zinc-carbon cell still greater. For this 
reason zinc and carbon, being cheap commercial products, 
are extensively used in batteries. The arrows indicate the 
direction of current through the internal and external circuits. 
In a lead-carbon cell the carbon would be the positive and 
the lead the negative terminal ; while in a lead-zinc cell the 
lead is the positive terminal and the zinc the negative termi- 
nal. Considering the plates in the list, any substance is pod* 
tive to any substance which follows it, and negative to any pre- 
ceding it. 



VOLTAIC ELECTRICITY. 61 

Exp. 13 : Using some similar strips of lead, copper, carbon, and 
zinc, make up different types of cells in dilute sulphuric acid. Con- 
nect each combination to the detector galvanometer and note the 
direction that the needle swings, the value of the deflection, and to 
which terminal each plate was connected. Note that when lead is 
connected to the same terminal of the galvanometer, and carbon used 
with it, the deflection is in the opposite direction to that when zinc is 
used with lead, which illustrates that in one instance the current 
leaves the lead terminal (+), and in the other instance flows to 
it (-)• 

Student's Experimental Cell. — A simple form of experimental cell 
with which numerous experiments can be made is illustrated in 
Fig. 76-A. A glass U tube is clamped to a vertical block on a base 
support by means of a rubber band. Suitable connections on the top 
of the block afford means for rapidly insert- 
ing rods, of the different metals in the electro- 
chemical series, in the electrolyte held in the 
U tube, and the chemical action is clearly 
visible. The device may be used as an electro- 
lytic cell, also as a calorimeter when an iron 
wire spiral is inserted in the tube, and, again, 
as a convenient fuse block for determining 
the heating and fusing effects of the current 
on the different metals. 

Exp. 14 : Connect a galvanometer wound 

with many turns of fine wire to a Volta cell 

Fig. 76-A.— Student's and note the value of the needle's deflection. 

Experimental Cell. Slowly withdraw the plates from the liquid 

and you note that the deflection of the needle 

remains the same until the circuit is broken at the surface of the 

liquid. This proves that the E. M. F. is independent of the area of 

the plates immersed. (See fl 74.) Move the plates further apart or 

closer together and the deflection is not changed, if the galvanometer 

is wound as above. The E. M. F. of a cell is independent of the 

distance between the plates. 

75. Local Action. — When a pure piece of zinc (which it 
is difficult to obtain) is used in a cell there is no action 
at the zinc except when the cell is in use. The ordi- 
nary commercial zinc contains many impurities, such 
as small particles of carbon, iron, tin, lead, etc., and 
when a rod of such zinc is placed in a cell these 
foreign particles form numerous local voltaic cells on 
the surface of the zinc inside the cell, with the result 
that the zinc is being continuously eaten away, Fig. 77. 
whether the cell is in action or at rest. These small ^i?n 
currents divert just so much strength from the regular 
battery current, thereby weakening it. Fig. 77 illustrates a 
magnified particle of iron on a zinc rod, and a local current 




62 PRACTICAL ELECTRICITY. 

would flow from the iron to the zinc through the solution and 
from the zinc to the iron across the junction. This is known 
as local action. In some cells local action is also caused by 
a difference in the density of the liquid at various parts of 
the cell. In this case the zinc near the top of the liquid is 
ordinarily wasted away, and may be entirely eaten off. 

76. Amalgamation. — Local action may be prevented by 
thoroughly cleaning the zinc with sand paper, then immersing 
it in. dilute sulphuric acid and while still wet applying mercury 
(quicksilver) by means of a rag swab. A bright amalgam 
is formed over the surface of the zinc and it is said to be 
amalgamated. The mercury dissolves the outer layer of zinc, 
forming a zinc-mercury amalgam. The foreign particles are 
either covered up from the action of the acid, or drop down 
to the bottom of the cell, or carried off by any remaining 
local action. The mercury does not prevent the zinc from 
being dissolved during the action of the cell, but continues to 
re-form an amalgam as the zinc wastes away. Zinc for bat- 
tery plates is sometimes cast with a small percentage of mer- 
cury in its composition. 

QUESTIONS. 

1. Explain what you understand by the word electricity. 

2. How does electricity manifest itself? 

3. What is the action of dilute sulphuric acid on zinc? 

4. What is a simple cell ? 

5. Explain the action in a simple voltaic cell. Give sketch. 

6. Give your idea of a ''current" of electricity. 

7. What is an electrolyte? 

8. Describe and illustrate Yolta's pile. 

9. What is meant by an open and closed circuit? 

10. Distinguish between the internal and external circuit of a cell. 

11. What are insulators? 

12. What is meant by a good conductor ? 

13. State an experiment you would make to determine whether a 
body was an insulator or a conductor. 

14. Give a reason for attributing direction to a current. 

15. Which way does a current flow inside a Volta cell? 

16. Sketch a simple Volta cell, name all the parts, and show the 
direction of the current in the internal and external circuit. 

17. Distinguish between poles and plates. 

18. Which is the negative electrode in a lead-copper cell in 
H 8 S0 4 ? 

19. Which is the positive plate in a lead-iron cell? 

20. What is a detector galvanometer, and for what is it used ? Give 
sketch. 



LESSON IX. 

BATTERIES. 

Primary Batteries— Open Circuit Cells— Closed Circuit Cells — Reme- 
dies for Polarization— The E. M. F. of Cells — Smee Cell— Bichro- 
mate Cell — Fuller Bichromate Cell— Partz Acid Gravity Cell — 
Bunsen's and Grove's Cells — Daniell's Cell — Leclanche Cell — 
Gonda Leclanche Cell— Carbon Cylinder Cell — Edison-Lalande 
Cell — Chloride of Silver Cell— Dry Cells— Classification of Cells 
— Chemicals for Cells and Some Chemical Symbols — Questions. 

77. Primary Batteries. — Primary batteries are so called to 
distinguish them from secondary batteries (storage batteries 
or accumulators, ^[ 107). Primary batteries are divided 
into two general classes, according to the manner in which 
they are to be used, known as open circuit cells and closed 
circuit cells. 

78. Open Circuit Cells. — Open circuit cells are used for 
intermittent work, where the cell is in service for short periods 
of time, such as in electric bells, signaling work, and electric 
gas lighting. In cells of this class polarization does not have 
much opportunity to occur, since the circuit is closed for 
such a short period of time ; hence, these cells are always 
ready to deliver a strong current when used intermittently. 
If kept in continuous service for any length of time the cell 
soon polarizes or " runs down," but will recuperate after re- 
maining on open circuit for some little time. 

79. Closed Circuit Cells. — In the closed circuit type of 
cell, polarization is prevented by chemical action, so that the 
current will be constant and steady till the energy of the 
chemicals is entirely expended. This type of cell is adapted 
for furnishing current continuously, as in the service of small 
lamps, motors, electroplating, etc. 

80. Remedies for Polarization. — In the simplest form of 
cell, as zinc, copper, and dilute sulphuric acid, no attempt 
has been made to prevent the evil of polarization, ^[ 73 ; 
heuce, it will quickly polarize when the circuit is closed for 
any length of time, and may be classified as an open circuit 

63 



64 PRACTICAL ELECTRICITY. 

cell. When polarization is remedied by chemical means, 
the chemical added is one that has a strong affinity for 
hydrogen and will combine with it, thus preventing the cov- 
ering of the negative plate with the hydrogen gas. The 
chemical used for this purpose is called the depolarizer and 
may be used either in a solid or liquid form, which gives rise 
to several forms of cells, such as cells with a single fluid, 
containing both the acid and the depolarizer ; cells with a 
single exciting fluid and a solid depolarizer, and cells with 
two separate fluids. (See ^[ 94.) 

In the double fluid form of cell the zinc is immersed in 
the liquid (frequently dilute sulphuric acid) to be decom- 
posed by the action upon it, and the negative plate is sur- 
rounded by the liquid depolarizer, which will be decomposed 
by the hydrogen gas it arrests, thereby preventing polariza- 
tion. The two liquids are sometimes separated by a porous 
partition of unglazecl earthenware, keeping the liquids from 
mixing, except very slowly, but not preventing the passage 
of hydrogen or electricity. 

Place sufficient mercury in a small battery jar to cover the bottom 
and fill the jar with a sal-ammoniac solution. Suspend a piece of zinc 
from the top of the jar and you have a zinc-mercury cell. Make con- 
nections with the mercury by a piece of rubber-covered wire. Con- 
nect the cell to a short coil galvanometer and note the falling deflec- 
tion of the needle, due to polarization. When the cell becomes 
sufficiently polarized drop into the solution a piece of mercuric 
chloride (HgCl 2 ) the size of a pin head. The galvanometer needle 
instantly shows a much larger deflection. The hydrogen has been 
removed by the chlorine in the mercuric chloride. When the 
chlorine becomes exhausted polarization sets in again. The mer- 
curic chloride is thus a chemical depolarizer. 

81. The E. M. F. of Cells. — Considering the electromotive 
force of one particular type of cell as a standard of E. M. F. , 
another type of cell will possess either a greater or less force 
in comparison with it. The unit of electromotive force is 
called the volt, and is about the pressure set up by a Volta 
cell, so that if a cell has an E. M. F. of 1.4 volts we mean 
that it possesses 1.4 times the force of a Volta cell. Cells 
are, therefore, rated by their E. M. F. In ^[136 will be 
found a table of E. M. F.'s of the different types of cells. 

82. Smee Cell. — This cell is an example of the mechani- 
cal means used to overcome polarization. A plate of lead or 
silver is suspended between two zinc plates in dilute sul- 



BATTERIES. 



65 




Fig. 78.— Smee 
Cell. 



phuric acid. The silver or lead plate is covered with a fine, 

powdery deposit of platinum, which gives the surface a 

rough character, so that the bubbles of hydrogen will not 

readily adhere to it as they are formed, but 

rise to the surface of the solution. Another 

mechanical method to overcome polarization 

is to rotate the electro-negative plate, thus 

preventing bubbles of gas from adhering to 

it ; but as this necessitates a constant force 

to keep the plate in motion, the cell would 

not be very economical. No mechanical 

method can wholly prevent the collection of 

hydrogen on the negative plate. This can 

only be accomplished by furnishing some 

chemical with which the hydrogen, as soon 

as it is liberated, will combine. The E. M. F. 

of a Smee cell is about 0.65 volt. 

83. Bichromate Cell. — In this type of cell polarization is 
prevented by chemically arresting the hydrogen gas, so that 
it never reaches the negative plate. The same will be true of 
most of the cells now to be described. Bichromate of soda 
or bichromate of potassium is the depolarizer, to which is 
added water and sulphuric acid for attacking the zinc. The 
bichromates are rich in oxygen, for which hydrogen has a 
strong affinity. Carbon and zinc plates are used, and. this 
type made up in several forms and termed chromic acid cells. 
In the Grenet (Gren-a/) form a zinc plate is suspended by a 
rod between two carbon plates, Fig. 79, so that it does not 
touch them, and when the cell is not in use the zinc is with- 
drawn from the solution by raising and fastening the rod by 
means of a set-screw, as the acid attacks the zinc when the 
cell is on open circuit. This cell has an E. M. F. of over 2 
volts at first, and gives a strong current for a short time, but. 
the liquid soon becomes exhausted, as will be noted by the 
change in the color of the solution from an orange to a dark 
red, and must be replenished. The zinc should be kept well 
amalgamated and out of the solution except when in use. 
It is a good type of cell for experimental work, and about two 
cells would perform nearly all of the experiments in this 
book. A simple substitute for this type of cell would be a 
number of electric light carbons fastened together to form 
the negative 'plate and several zinc rods for the positive 



66 



PRACTICAL ELECTRICITY. 




plate, which could be removed at will and then rinsed in 

water. 

To make a solution for a bichromate cell take 3 ounces of 

finely powdered bichromate of potash and 1 pint of boiling 
water; stir with a glass rod, and after 
it is cool add slowty, stirring all the 
time, 3 ounces of sulphuric acid. The 
solution should not be used until cool. 
In mixing a battery solution always pour 
the acid gently into the water, while stirring, 
to dissipate the heat. Never pour water 
into acid. If bichromate of soda is used 
as above take 4 ounces bichromate of 
soda, 1 \ pints boiling water, and 3 ounces 
of sulphuric acid. These battery solu- 
tions are sometimes termed electropoin 
fluids. 

84. Fuller Bichromate Cell.— This 
double fluid cell has the advantage over 
the Grenet type, in that the zinc is always 
Fig. 79.— Grenet Cell, kept well amalgamated and does not 
require removal from the solution. A 
pyramidal block of zinc, to which a 

metallic rod covered with gutta-percha is attached, is placed in 

the bottom of a porous cup, Fig. 80, and an ounce of mercury 

is poured in. The cup is filled with a very dilute solution 

of sulphuric acid or water, and 

then placed in a glass or earthen 

jar containing the bichromate 

solution and the carbon plate. 

The acid diffuses through the 

porous cup rapidly enough to 

attack the zinc, which, being 

well amalgamated, prevents local 

action. The hydrogen travels 

from the zinc through the porous 

cup and combines with the 

oxygen in the potassium bi- 
chromate. The E. M. F. is about 

2.14 volts, and the cell is used 

for open circuit or semi-closed circuit work. 

of the Fuller type is shown in Fig. 81. 



Zinc and carbon in bi- 
chromate solution. 




Fig. 80— Fuller Cell. 

Zinc in dilute H 2 S0 4 in porous cup, 

carbon in a bichromate solution. 



Another form 



BATTERIES. 



67 



85. Partz Acid Gravity Cell. — In the Partz acid gravity 
form of cell, Fig. 81-A, the electrolyte which surrounds 
the zinc is either magnesium sulphate or common salt. 




Fig. 81.— Fuller Cell. 
Zinc in porous cup with mercury and dilute H 2 S0 4 , carbon in a bichromate solution. 

The depolarizer is a bichromate solution which surrounds 
the perforated carbon plate located in the bottom of 
the jar. A vertical carbon rod fits 
snugly into the tapered hole in the 
carbon plate, and extends through 
the cover forming the positive pole. 
The depolarizer, being heavier than 
the electrolyte, remains at the 
bottom of the jar, and the two 
liquids are thus kept separate. This 
depolarizer is placed on the market 
in the form of crystals, known as 
sulpho-chromic salt, made by the 
action of sulphuric acid upon 
chromic acid. When dissolved, its 
action is similar to that of the 
chromic acid solution. After the 
cell has been set up with everything 
else in place the crystals are intro- 
duced into the solution, near the bottom of the jar, through 
the vertical glass tube shown, and slowly dissolve and diffuse 
over the surface of the carbon plate. When the cell cur- 




Fig. 81-A.— Partz Cell. 



68 



PRACTICAL ELECTRICITY. 



rent weakens a few tablespoonfuls of the salt introduced 
through the tube will restore the current to its normal value. 
The cell should remain undisturbed to prevent the solution 
from mixing. Its E. M. F. is from 1.9 to 2 volts, and the 
6 in. x 8 in. size has an internal resistance of about .5 ohm. 
Since the depolarization is quite effective, the cell may be 
used on open or closed circuit work. 

86. Bunsen and Grove Cells. — These cells are examples 
of the two fluid type, in which the solutions are separated 
by a porous partition. Bunsen's battery has a bar of 
carbon immersed in strong nitric acid contained in a porous 
cup. This cup is then placed in another vessel containing 




Platinum 




Fig. 82.— Bunsen Cell. 

Carbon in HN0 3 porous cup, zinc in 
dilute H 2 S0 4 . 



Fig. 83.— Grove Cell. 

Platinum in HN0 3 in porous cup, 
zinc ia dilute H 2 S0 4 . 



dilute sulphuric acid, and immersed in the same liquid is a 
hollow, cylindrical plate of zinc, which nearly surrounds the 
porous cup. The hydrogen, starting at the zinc, traverses, 
by composition and recom position, the sulphuric acid, passes 
through the porous partition, and immediately enters into 
chemical action with the nitric acid, so that none of it reaches 
the carbon. There are produced by this action water, which 
in time dilutes the acid, and orange-colored poisonous fumes 
of nitric oxide, which rise from the battery. If the nitric 
acid first be saturated with nitrate of ammonia, the acid will 
last longer and the fumes be prevented. Strong sulphuric 
acid cannot be used in any battery ; generally 12 parts by 



BATTERIES. 



69 



weight, or 20 by volume, of water are added to one part of 
sulphuric acid. 

Grove used a strip of platinum instead of carbon in his cell. 
A solution of bichromate of potassium (as in ^| 83) is fre- 
quently substituted for the nitric acid in the porous cup, 
thereby avoiding disagreeable fumes. Bunsen's and Grove's 
batteries produce powerful and constant currents, and are well 
adapted for experiments, but they require frequent attention, 
and are expensive, so that they are little used for work of 
long duration. E. M. P., of these cells, 1.75 to 1.95 volts. 

87. Daniell Cell. — This battery is made in many forms 
and called by various names, such as Gravity battery, Blue- 
stone Cell, Crowfoot battery, etc. An explanation of the theory 



Galvanometer 



e 



(+) 



milium 



lief ore- ArCl ion- 



r * r \of_Coppi 



Iphale ") 




$T_0 Current 



■Stilph 



vric-l 



mm 



OQdy 



VBZBSSB? ^5SZ> 



Ouring-AiXion- 



m 



siudpf Cnpper\ 



trrenCHassin^ 



}- Sulphuric \ J - 
(- Acid- >- 5*Tc 



Z^22Z Z Z 



Fig. 84. — Chemical Action in the Daniell Cell when the Circuit is Closed. 

of a simple form will answer for all forms of this class, and it is 
of importance, since the cell is much used in practice forgiv- 
ing constant currents of long duration. It is, therefore, a 
closed circuit battery. Zinc and copper elements are used. 
In Fig. 84 they are separated by a thin partition of unglazed 
pottery. On the zinc side of the partition is put dilute sul- 
phuric acid (H 2 S0 4 ), or simply water, if the cell is not 
required for immediate use ; on the copper side is placed 
sulphate of copper (CuS0 4 ), dissolved in water, together with 
some sulphate of copper crystals (bluestone) to maintain the 
supply of copper sulphate solution. When the circuit is 
closed, as shown by Fig. 84, the zinc combines with the 
(S0 + ) of the sulphuric acid forming sulphate of zinc 
(ZnSO ), and thus sets free the two molecules of hydrogen 
(H 2 ). 



"0 



PRACTICAL ELECTRICITY. 



This hydrogen gas passes through the porous partition, 
but instead of collecting on the sides of the copper plate, 
it meets with the sulphate of copper (CuS0 4 ), and having a 
greater natural affinity for the (S0 4 ) than the copper (Cu) 
possesses, it displaces the copper, and forms sulphuric acid, 
(H 2 S0 4 ) setting free pure metallic copper, which is deposited 
upon the copper plate. This continuous extraction of metal- 
lic copper from the solution would soon weaken it, were it 
not for the fact that the copper crystals dissolve and thus 
automatically keep the solution saturated. To maintain a 





Gravity Daniell Cell. 



Fig. 85. 



Student's Porous Cup 
Daniell Cell. 



constant current for an indefinite time, therefore, it is only 
necessar}^ to keep the supply of copper crystals and zinc 
maintained. The cell has an E. M. F. of about one volt and 
gives a small, but steady current. The " gravity type " of 
this cell, which is used in this country for telegraphy (closed 
circuit work), is illustrated in Fig. 85. 

A student's small Daniell cell is also shown in Fig. 85. It is of the 
double fluid type. A rod of freshly amalgamated zinc is placed in 
the porous cup in a solution of zinc sulphate, with a specific gravity 
of 1.1. The porous cup is placed in a glass jar containing a solution 
of copper sulphate of the same specific gravity, and surrounded by 
a sheet of copper. It is advisable to short-circuit the cell for about 
ten minutes before using. Under the above conditions the E. M. F. 
is 1.05 volts. The cell should be set up with a new solution each 
time it is required and taken apart and cleaned after use. The cur- 



BATTERIES. 



1 



rent on short circuit is small, about J ampere, but since polarization 
is eliminated it is a good cell to use for electrical measurements 
where a constant source of E. M. F. is required, as in Lesson XXI. 

88. Leclanche Cell. — This very common form of cell is 
an example of the single solution type, with a solid depolar- 
izer surrounding the negative element, which is generally 
carbon, the positive element 
being zinc, Fig, 86. The 
liquid used is a strong solution 
of ammonium chloride, com- 
monly known as sal-ammoniac, 
and much resembles table 
salt. In the porous cup type 
of cell, a carbon slab is placed in 
the porous cup and surrounded 
by a mixture of small pieces 
of carbon and manganese 
dioxide, the top being covered 
by means of pitch, leaving one 
or two small holes for air and 
gas to pass through. The 
depolarizer will take care of a 
limited amount of the hydro- 
gen produced when the cell is 
on closed circuit, but if the 
circuit be closed for any length 
of time polarization occurs. 
The cell is thus of the open 
circuit class, and will furnish a 
good current where it is required only intermittently. Zinc 
is dissolved only when the cell is being used. This type of 
cell, or its modification, is used for gas lighting and bell 
work. The cell requires very little attention. Water must 
be added as the solution evaporates, and the zinc rod 
replenished when necessary. The. E. M. F. is about 1.48 
volts and the internal resistance is about 4 ohms. 

Directions for setting up the Leclanche Cell. — 1. Place in the 
glass jar six ounces of ammonium chloride (sal-ammoniac), pour in 
water until the jar is one-third full and stir thoroughly. 

2. Put in the porous cup, and add water if necessary until the 
level of the water is within 1J inches of the top of the porous cup. 

3. Put the zinc in place and set the cell away, without connecting 
up, for ten or twelve hours, to allow the liqufd to thoroughly soak 




Fig. 86.— Leclanche Cell. 

Carbon in porous cup with Mn0 2 , zinc 
in sal-ammoniac solution. 



72 



PRACTICAL ELECTRICITY. 



into the porous cup, which will lower its level to about two-thirds 
the height of the jar, at which level it should be kept, by adding 
water as it evaporates. The cell is then ready for use. 

89. Gonda Leclanche Cell.— This cell is a modification 
of the porous cup type, in which the manganese has been 
mixed with some gelatinous binder, and 
compressed into slabs, under hydraulic 
pressure. Two such slabs or prisms, one 
on each side of the carbon plate, are held in 
position by rubber bands, Fig. 87. A zinc 
rod and a sal-ammoniac solution are used. 
This cell was designed to dispense with the 
porous cup. 

90. Carbon Cylinder Cell.— Carbon 
possesses a natural power to prevent a 
limited amount of polarization by absorbing 
the hydrogen gas coming from the zinc rod, 
so that we find it used in a variety of shapes 
for open circuit cells, which gives rise to as 
many different names, such as Samson, 
Hercules, Law, National, Standard, etc. 

In all these types of cells, Fig. 88, sal- 
ammoniac and zinc are used, and by corrugating the carbon, 
fluting it, or making concentric cylinders, special merits are 
obtained in each case. Fig. 89 illustrates a carbon cylinder 




Fig. 87.— Gonda 
Leclanche 
Elements. 




Fig. 88. — Elements of a Carbon Cylinder Cell. 
Zinc, carbon and sal-ammoniac solution. 



BATTERIES. 



73 



carbon is made 
with oxide of 



cell of the Standard Carbon Co., in which the 

in the form of a porous cup and then fillec 

manganese to prevent polarization. Still another form of the 

same make is shown in Fig. 90, in which the space between the 

two concentric carbon cylinders has been filled with oxide of 





Fig. 89. — Elements of Carbon Cylinder Cell with Depolarizer. 
Zinc, manganese dioxide in a porous cup and sal-ammoniac solution. 

manganese and then sealed in. The zinc rod is prevented from 
touching the carbon by being first inserted through a porce- 
lain insulator. About 4 to 6 ounces of sal-ammoniac are gen- 
erally used for cells of ordinary size. The salt is placed in 
the jar, water poured in until it is about 
two-thirds full, and then stirred till all the 
salt is dissolved. When the carbon cylinder 
is inserted the solution should be w T ithin \\ 
inches of the top of the jar. These cells 
should not be put in w r arm places, as over 
the heater in a cellar, on account of the 
rapid evaporation of the electrolvte. The 
E. M. F. is from 1.4 to 1.6 volts for the 
different forms of this type. 

91. Edison-Lalande Cell. — As in the 
Leclanche type, this cell is a single fluid 
battery with solid depolarizer, but is ad- 




Fig. 90. 



Section through car- 

mirably adapted for use—im closed circuit bnn cylinder showing 

i p -ii i • MnOo depolarizer. 

work, as tor small motors, electrotypmg, 
telegraphy, etc. Zinc is the positive, and black oxide of 
copper (CuO), the negative element. The exciting liquid 
is a solution of caustic potash. The oxide of copper is ob- 
tained by the process of roasting copper turnings ; it is then 



74 



PRACTICAL ELECTRICITY. 



ground into a fine powder and compressed into solid blocks, 
from which plates of a suitable size are cut. 

These plates are suspended from the cover of the battery jar, 
Fig. 91, by a light framework of copper, one end of the frame- 
work terminating as the positive pole of the battery. On 

each side of the copper oxide 
element is suspended a zinc 
plate, which is prevented from 
coming into contact with the 
copper oxide plate by means of 
vulcanite buttons. When the 
circuit is closed and the cell in 
action, the water is decom- 
posed, the ox}^gen, forming 
with the zinc, oxide of zinc, 
which in turn combines with 
the potash to form a double 
salt of zinc and potash, which 
dissolves as rapidly as it is 




Fig. 91.— Edison-Lalande Cell. 
Zinc and copper oxide in caustic 
potash solution. 



formed. The hydrogen lib- 
erated by the decomposition 
of the water reduces the 
copper oxide to metallic copper. The reduced copper is 
of great purity and can again be converted into copper oxide. 
It is important to see that the oxide plates are entirely sub- 
merged in the caustic potash solution. Heavy paraffin oil 
is poured on top of the solution, so as to form a layer about 
one-quarter inch deep on the surface, to keep out the air. 
When oil is not used creeping salts are formed and the life 
of the battery is reduced fully two-thirds. The E. M. F. is 
low, only 0.7 of a volt, but the internal resistance is also very 
low, so that quite a large current can be drawn from the cell. 
It is made in a number of different sizes, ^| 140. 

92. Chloride of Silver Cell. — This cell is another exam- 
ple of the single fluid type with a solid depolarizer, and is 
used extensively in portable testing sets where a large num- 
ber of small cells are mounted in a case. The elements are 
small wires, or rods of zinc and silver, and on the silver is 
cast the solid depolarizer, silver chloride, which is reduced 
to metallic silver by the hydrogen gas. The chloride of sil- 
ver may be melted in a porcelain crucible and cast around 
the wire in a carbon mold. A small cylinder of vegetable 



BATTERIES. 



75 



parchment surrounds the silver wire and the chloride, to pre- 
vent internal short circuits. The zinc rod and silver wire 
are held in a paraffin stopper, the silver wire of one cell being 
wedged into the zinc rod of the next, and. so on, when a number 
are connected in series. The elements are sealed in a small 
glass tube containing the electrolyte, which may be zinc sul- 
phate, zinc chloride, or caustic potash. 
With zinc sulphate the E. M. F. is 1.1 volts. 

93. Dry Cells. — These cells differ from 
those already described, in that the exciting 
fluid is combined with some special ab- 
sorbent, such as sawdust, etc., or is made 
into a jelly. In the Gassner type of cell 
the zinc element is in the form of a cylinder, 
which holds the other element (carbon) 
and the exciting mixture. The carbon rod 
or plate occupies about one-half the space 
in the cell, and the space between the carbon 
and zinc cylinder is tilled with the following 
mixture, the proportions being by weight : 
Oxide of zinc, 1 part ; sal-ammoniac, 1 part ; 
plaster, 3 parts ; chloride of zinc, 1 part ; 
water, 2 parts. Dry cells being portable, 
are very convenient for use where only an intermittent 
current is required. The E. M. F. is about 1.4 volts. 

94. Classification of Cells. — 

Batteries \ J' 

I Secondary. 

Primary batteries : 

Classified by f Open circuit cells — (Grenet, Leclanche. ) 

polarization •< Closed circuit cells — (Daniell, Lalande, 

into ( Fuller.) 

f Single fluid cells — (Grenet, Leclanche, 

J Lalande.) 

j Double fluid cells — (Bunsen, Grove, 

L Daniell, Fuller. ) 

C Liquid depolarizer — (Grenet type.) 

Single fluid cells with -j Solid depolarizer — (Leclanche, La- 

(_ lande.) 

Double fluid cells with liquid depolarizer — (Bunsen, Grove, 

Daniell. ) 




Fi2 



Dry Cell. 



Classified by 
construction 
into 



76 PRACTICAL ELECTRICITY. 

95. Chemicals for Cells and Some Chemical Symbols.— 

Copper Sulphate (blue vitriol), CuS0 4 

Zinc Sulphate (white vitriol), ZnS0 4 

Ammonium Chloride (sal-ammoniac), NH 4 C1 

Bichromate of Soda, Na 2 Cr 2 7 

Bichromate of Potassium, K 2 Cr 2 7 

Chromic Acid, Cr0 3 Lead Peroxide, Pb0 2 

Caustic Potash, KOH Sulphuric Acid, H 2 S0 4 

Caustic Soda, NaOH Nitric Acid, HN0 3 

Copper Oxide, CuO Hydrochloric Acid, HC1 

Manganese Dioxide, MnO Silver Chloride, AgCl 

Lead Oxide, PbO Zinc Chloride, ZnCl 2 

QUESTIONS. 

1. Since the hydrogen gas is evolved from the zinc when it is 
placed in dilute acid, how do you account for the fact that in a Volta 
cell when connected to a circuit, the hydrogen gas is evolved at the 
copper plate, yet the copper is not attacked by the acid ? 

2. Upon what does the E. M. F. of a cell depend? 

3. Would you expect a very large cell to have the same E. M. F. 
as a small one of the same kind made up in test tube ? Why? 

4. Give a list of some materials used in cells, in the order of their 
potential difference in dilute sulphuric acid. 

5. A cell is composed of copper and iron in dilute sulphuric acid. 
Draw a sketch indicating the + and — plates and electrodes, and the 
direction of current, when the plates are connected. 

6. Of what use is local action in a cell ? How is it prevented ? 

7. What is the distinction between open and closed circuit cells? 

8. Why are there so many different makes of cells on the market, 
and what is the general distinction between them ? 

9. Describe a two-fluid cell. Give an example. 

10. What is a depolarizer ? Give an example of a cell with a solid 
and liquid depolarizer, and state how the depolarizer acts in each. 

11. Describe the Daniell cell and illustrate the chemical action. 

12. Describe a bichromate cell of the Grenet type. Make a sketch. 

13. How does the Fuller cell differ from the Grenet cell, since the 
chemicals and plates used are identical? 

14. Describe the Leclanche porous cup type of cell. How is polari- 
zation prevented in this cell ? 

15. How does the Edison-Lalande cell differ from the Leclanche 
cell, since they both use solid depolarizers? 

16. Which of the two cells mentioned in question 15 would you use 
for a spark-ignitor on a gas engine? 

17. In what respect does a dry cell differ from a fluid cell? 

18. Form a table of all the cells you know of. giving the -f- and — 
plates, electrolyte used, depolarizers, name and type (open or closed 
circuit) in the different columns of the table. 

19. Describe fully the action of the Edison-Lalande cell. 



LESSON X. 

ELECTROLYSIS. 

Effects of the Current— Heating Effect — Magnetic Effect— Chemical 
Effect— Electrolysis— Electrolysis of Copper Sulphate — Electro- 
lysis of Zinc Sulphate — Electrolysis of Lead Acetate — Electroplat- 
ing — Electrotyping — Polarity Indicator — Secondary Batteries, 
Storage Batteries or Accumulators— Direction of Current in an 
Accumulator on Charge and Discharge— Commercial Storage Bat- 
teries — Questions. 

96. Effects of the Current. — A current of electricity is 
not a material substance, and, therefore, has no dimensions 
(length, breadth, or weight) by which it can be studied or 
measured. An electric current is studied by the effects it pro- 
duces, all of which are commercially utilized. The effects mani- 
fested by a current of electricity are : Heating Effect, Magnetic 
Effect, Chemical Effect, and Physiological Effect. The first three 
of these effects are treated in this book. A current passed 
through the body produces muscular contractions, which are 
said to be due to the physiological effect. Electro-therapeu- 
tics deals with the study of this effect. 

By a direct or continuous current is meant one which flows 
always in the same direction and has the same strength, 
as, for example, the current from a battery. In a pulsating 
current the direction is uniform, but the current strength 
varies. Most direct current dynamos furnish a pulsating cur- 
rent, but the pulsations are so rapid that the current becomes 
practically continuous. In an alternating current the direc- 
tion is reversed at short intervals, and the current strength 
also varies periodically. Dynamos, called alternators, furnish 
such a current. The variations occur so rapidly that the 
current appears to be constant in the circuit.* 

97. Heating Effect.— 

Exp. 15 : Connect the terminals of a bichromate cell to a piece of 
No. 32 iron wire about one inch long. The wire becomes so hot that 

*Tn most of the following pages the references to current strength are true for direct 
currents, and exceptions must be made if other currents are considered, 

77 



78 PRACTICAL ELECTRICITY. 

it is luminous, illustrating both the heating and lighting effects of a cur- 
rent of electricity. The chemical energy inside of the cell is thus con- 
verted into electrical energy outside of the cell in the form of heat 
and light. If the current is strong enough the wire will be entirely 
melted. 

Exp. 16 : Substitute a piece of copper wire of the same size and 
length as the iron wire in Exp. 15. A smaller change of temperature 
will be noted. 

Exp. 17 : Close the circuit of the cell without any fine wire in the 
circuit. More heat is now generated inside of the cell than in the 
external conducting wires. 

Every wire which conducts a current of electricity becomes 
heated to some extent as a result of the current, because the 
best conductors offer some opposition (resistance) to the flow 
of the current, and it is in -overcoming this resistance that the 
heat is developed. If the wire is large in cross- 
sectional area and the current small, the heat 
developed will be so small in amount as not to 
be recognized by the touch, yet, nevertheless, 
some heat is evolved from the wire ; upon the 
other hand, with a small wire and a large current 
it becomes quite hot. As the heat increases 
with the resistance of the conductor used, by 
employing a poor conductor we obtain both light 
and heat. This principle is used in the incan- 
descent electric lamp, which consists of a fine 
filament of carbonized material inclosed in a 
glass bulb, from which the air has been ex- 
hausted, Fig. 93. The current is passed through 
Isje^ZL^Z&s the filament and heats it to a state of incan- 
Fig. 93.— Elec- descence. The globe is exhausted, thereby pre- 
tnc Incandes- ven ting combustion of the filament, which 
would occur if it were heated in the air. Of the 
electric energy expended in the lamp, only about 5 per cent 
is represented by the light emitted, while the balance appears 
as heat, so that such a lamp, while convenient, is not an 
efficient source of illumination. The heating effect of the 
current is also utilized in the various electric cooking utensils 
on the market, in electric welding, electric smelting, and in 
reducing metals from their ores. 

98. Magnetic Effect. — A wire carrying a current of elec- 
tricity deflects a magnetic needle. When insulated and coiled 
around an iron core the current magnetises the core. If the 
current flowing through a wire be sufficiently strong, the wire 




ELECTROLYSIS. 



79 



will attract iron filings, proving the existence of the magnetic 
field around the wire. This subject is treated under Electro- 
magnetism, Lesson XV. 

99. Chemical Effect. — We have noted in a simple Volta 
cell, If 71, how electrolytic decomposition takes place inside 
the cell when a current is flowing. The current is also capa- 
ble of decomposing certain chemical compounds (liquids) 
outside of the cell, when it is passed through them, breaking 
up the compounds into their constituent parts. Liquids may 
be divided into three classes : (1) Those which do not conduct 
electricity at all, such as many of the 
oils, particularly petroleum ; (2) liquids 
which conduct without decomposition, as 
mercury and molten metals, which 
conduct just as solids ; (3) liquids which 
are decomposed when they conduct a cur- 
rent, as the dilute acids, solutions of 
metallic salts, and some fused com- 
pounds. 

Exp. 18: Electrolysis of Water.— Fill 
the U tube, Fig. 94, with water, and add a 
few drops of sulphuric acid to make the 
liquid a better conductor. Connect the ter- 
minals of two bichromate cells joined in 
series, ][ 141, to the two platinum terminals 
shown in the U tube, so that the circuit from 
the cells will be completed through the 

acidulated water Have the corks quite Fig . 9 4.— Glass tl Tube with 
i?r u Se m u the y tl - be . f0r the , gases to escape. Electrodes Forming an 
When the circuit is completed bubbles of Electrolytic Cell, 

gas immediately rise from both platinum 

plates, more, however, from the platinum plate connected with the 
negative pole of the battery. The gases may be collected separately 
by the forms of apparatus shown in Figs. 99 and 100, or collected 
together in one tube in the form of voltameter shown in Fig. 97. 

During this electro-chemical action the current decomposes 
the water, liberating hydrogen gas at the negative battery 
pole, and oxygen gas at the positive battery pole. Twice as 
much hydrogen as oxygen gas is liberated. Water is com- 
posed of these two gases, hydrogen and oxygen, in the pro- 
portion of two parts of hydrogen to one of oxygen (or H 2 0) 
and the current breaks up the water into its constituent parts, 
Fig. 97. If brass or copper plates are used, the positive plate 
will be attacked by the action, and no oxygen will be evolved. 




80 PRACTICAL ELECTRICITY. 

Exp. 19 : Reverse the direction of the current through the solution, 
by changing the battery terminals, and note that the hydrogen and 
oxygen gases are now liberated on the opposite electrodes from Exp. 
18, which is another reason for supposing that the current has direc- 
tion ; the opposite deflections of the magnetic needle being a former 
proof. 

100. Electrolysis. — A large number of chemical com- 
pounds in a state of fusion, or dissolved in certain solvents 
can, like the acidulated water, be separated into their con- 
stituent parts by the passage of an electric current through 
them. Any substance that is capable of being decomposed 
by an electric current is called an electrolyte (as in a Volta 
cell) and the process is termed electrolysis (meaning loosen- 
ing by electricity). Plates of carbon, lead, platinum or 
other metals are used to conduct the current to and from the 
solution, according to the substance to be electrolyzed. 

These plates are called electrodes, and the plate by which 
the current enters the electrolyte is called the positive electrode 
or anode and the plate by which it leaves the solution is called 
the negative electrode or cathode. The constituent parts of the 
electrolyte which are liberated at the surface of the electrodes 
are called ions ; the ion liberated at the positive electrode being 
called the anion, and that which appears at the negative elec- 
trode the cathion. Any vessel or apparatus used for perform- 
ing or measuring electrolysis is called a voltameter. In the 
electrolysis of water hydrogen is the cathion and oxygen the 
anion. 

101. Electrolysis of Copper Sulphate. — 

Exp. 20 : Fill the U tube, Fig. 94, with a solution of copper sul- 
phate, made by dissolving some copper sulphate crystals (bluestone) 
in water, and subject the solution to electrolysis, as in the case of the 
water, using platinum electrodes. Metallic copper is deposited upon 
^ the negative electrode, that is the plate 
~"^ becomes copper-plated. Oxygen gas is 
liberated at the positive platinum electrode 
and sulphuric acid is formed. 




\% The chemical symbol for copper sul- 

j } phate is CuS0 4 and by electrolysis it is 

r ~> ■$ separated into Cu (metallic copper) 

" - ^* ta r and S0 4 (sulphion). The hydrogen 

Fig " 95 '~^e°ter r V ° lta " S as liberated at the negative plate dis- 
places the Cu of the CuS0 4 forming 
H 2 S0 4 (sulphuric acid), and deposes the Cu on the negative 
plate, while oxygen gas is liberated at the + platinum plate, 



ELECTROLYSIS. 81 

as before. If the action is allowed to continue for some time, 
all the metallic copper is taken from the solution and deposed. 
This will be noted by the solution changing from a deep to a 
pale blue, as the change gradually takes place from copper 
sulphate to sulphuric acid. The action is represented as 
follows : 

CuS0 4 = Cu -f S0 4 

Sulphate of copper becomes copper and sulphion 

S0 4 + H 2 = H 2 S0 4 + O 

Sulphion and water produce sulphuric acid and oxygen 

Exp. 21 : Reverse the direction of current in Exp. 20 and note that 
now the copper-coated platinum plate becomes the positive electrode, 
with a platinum plate for the negative electrode. The latter has 
metallic copper deposed upon it, while the former metallic copper on 
the positive plate is returned again to the solution. 

Exp. 22 : Substitute two copper electrodes for the platinum elec- 
trodes and repeat Exp. 20. Metallic copper is again deposited upon 
the negative electrode (increasing its weight) but from the positive 
electrode no gas is evolved, yet this plate wastes away, or is dissolved 
in the solution, thereby losing in weight. 

When a copper positive plate is used, the CuS0 4 is sepa- 
rated into Cu on the negative plate, and S0 4 which attacks 
the positive plate, and forms a new molecule of CuS0 4 (cop- 
per sulphate). Thus as a molecule of copper sulphate is 
decomposed, a new molecule is formed, keeping the solu- 
tion constant. Just as much metallic copper is thrown down 
into solution from the positive plate, as is taken from the 
solution and deposed on the negative plate. The art of electro- 
plating is based on the above experiments. 

102. Electrolysis of Zinc Sulphate.— 

Exp. 23 : Dissolve some crystals of zinc sulphate, ZnS0 4 (white 
vitriol) in water. Refill the U tube, Fig. 94, with this solution and 
subject it to electrolysis. Use platinum electrodes and metallic zinc is 
deposited upon the negative electrode and oxygen gas is evolved from 
the positive electrode. Reverse the direction of current. The pre- 
viously deposited zinc is deposed again into solution while the other 
electrode now receives a deposit of zinc. Oxygen gas is not evolved 
from the positive electrode till all of the zinc has been thrown down 
into solution. 

Exp. 24 : Repeat Exp. 23, using two zinc strips as electrodes, and 
note that the positive strip wastes away, and the negative zinc strip 
gains in weight. The action of the Edison electrolytic meter for 
measuring current is dependent upon this principle, being then a 
zinc voltameter. 



82 PRACTICAL ELECTRICITY, 

103. Electrolysis of Lead Acetate. — 

Exp. 25 : Prepare a solution of lead acetate, and pass it through 
filter paper to clear the solution. Fill the U tube, Fig. 94, and sub- 
ject it to electrolysis, using platinum electrodes. Metallic lead is de- 
posited at the negative plate, and oxygen gas appears at the positive 
plate. In addition to coating the platinum plate the lead will be de- 
posited in a beautiful tree-like form extending out into the solution 
from the negative plate. The solution becomes weaker as the ex- 
traction of metallic lead continues. When the current is reversed, 
the former positive plate receives the deposit in the " tree form," but 
oxygen gas is not now liberated from the positive plate, until the lead 
previously deposited is dissolved in the solution. This experiment is 
very suitable for illustration in a lantern projection cell, as well as for 
laboratory work. 

104. Electroplating. — The art of depositing a coating of 
metal upon any object is termed electroplating, and is based 
upon the principles of electrolysis already explained. The 
metal held in solution is always deposited on the object to be 
plated, which must be connected to the negative pole of the 
source of electricity, while a plate of the metal from which 
the coating is derived, as nickel, copper, gold, or silver is used 
as the positive plate. In plating with gold or silver the bath 
(electrolyte) is always alkaline, and generally a cyanide of 
the metal to be deposited is used for the solution. In plating 
an iron spoon with silver, for example, the iron is cleaned, to 
remove all dirt and grease, and then first receives a deposit of 
copper in a copper bath, as silver will not deposit upon iron. 
Articles of iron, steel, zinc, tin, and lead cannot be silvered 
or gilded unless first coated with a thin covering of copper. 
After a thin coating of copper, the spoon is transferred to a 
silver bath, properly connected up and a coating of the desired 
thickness deposited, after which it is cleaned and brightened 
on a buffing wheel. 

Other substances beside metals can be electroplated by 
first preparing the surface with a coating of powdered 
graphite, or plumbago, upon which metal can be depos- 
ited. A very low voltage is used in electroplating, since the 
character of the deposit depends upon the density or strength 
of current used, ^[ 123. If electrolytic action takes place too 
rapidly, the deposit is soft, coarse-grained, and liable to prove 
unsatisfactory, while a small current gives a good, hard, close- 
grained deposit. The potential varies with the electrolytes 
used, generally from 1 to 3 volts being applied to the bath. 

105. Electrotyping. — Suppose an electrotype is desired 



ELECTROLYSIS. 83 

from a column of standing type. An impression in wax, or 
plaster of Paris, is carefully made of the type, and the wax 
mould dusted over with powdered graphite to make the 
surface a conductor. The mould is connected as the negative 
plate in a copper plating bath and receives a thin coating of 
metallic copper. After removal from the bath the copper 
deposit is removed from the mould and backed, or filled in 
with type metal to about the depth of one-eighth inch. When 
cool, the back is planed smooth, fastened to a block of wood, 
and can then be used in the press. The copper mould is 
generally so thin that it is necessary to back it up with the 
type metal, owing to the pressure to which the electrotype is 
to be subjected. In this manner the electrotypes for the 
pages of many books are made from the standing type, and 
may be used for taking thousands of impressions. 

106. Polarity Indicator. — The positive and negative poles 
of a direct current electric light, or power circuit, can be 
determined by dipping the terminals, at some little distance 
apart, into a tumbler of water. As twice as much hydrogen 
gas is evolved at the negative wire as oxygen at the positive 
wire, the polarity of the circuit is readily determined. Care 
must be taken not to bring the wires into contact, or some 
damage would occur, due to too much current flowing through 
such a low resistance circuit. A solution of iodide of potas- 
sium, with a little starch added, is sometimes sealed in a glass 
tube and terminals provided, by which a current can be passed 
through, and the polarity of the circuit determined. This is 
called a polarity indicator. Iodine is liberated at the positive 
terminal and turns the starch blue around this terminal. 

107. Secondary Batteries, Storage Batteries or Accu- 
mulators. — 

Exp. 26.— Place two copper strips in a solution of zinc sulphate 
contained in a small battery jar. Connect the terminals of the copper 
strips to a galvanometer, and note that the needle is not deflected, 
because the combination does not conform to the definition of a vol- 
taic cell, ^ (53. Disconnect, and substitute for the galvanometer, 
two bichromate cells connected in series (connect carbon to zinc). 
By electrolysis, hydrogen gas would be evolved at the negative plate, 
but having a greater affinity for the S0 4 part of the zinc sulphate 
(ZnSOJ, than the zinc, it displaces it, forming sulphuric acid (H 2 S0 4 ) 
and metallic zinc is deposed on the negative copper plate. After the 
action continues a little while, disconnect the battery and again con- 
nect the electrolytic cell to the galvanometer and note that the needle 
is now deflected. 



84 PRACTICAL ELECTRICITY. 

A secondary battery, storage battery or accumulator, is a 
voltaic cell, the positive and negative plates of which are 
formed or deposited by electrolysis, produced by a separate 
source of electricity. No electricity was stored in Exp. 26, but 
a chemical action took place, which changed the plates into 
two dissimilar metals and the salt (zinc sulphate) into an 
acid, capable of attacking one of them, thus conforming to 
the definition of a primary cell. The current performing the 
electrolysis is termed the charging current, and the secondary 
cell is said to be charged, meaning that it will again generate 
current when connected to a circuit. This is called discharg- 
ing the cell. The chemical action on discharge of our simple 
type of accumulator will be obviously the same as in the 
Volta cell, since the plates (copper- zinc) and the acid formed 
(sulphuric) are identical with the Volta cell. On discharge, 
the zinc is decomposed by the acid, and when it is all dis- 
solved in the solution the cell is entirely discharged and must 
be re-charged again by electrolysis. 

108. Direction of Current in an Accumulator on 
Charge and Discharge. — Upon charging the accumulator, 
Exp. 26, the direction of current inside the cell was from 
copper to zinc ; upon discharge, the current inside the cell 
travels in the opposite direction (zinc to copper, as in a Volta 
cell), so that the positive terminal of an accumulator is con- 
nected to the positive terminal of the charging lines, and this 
same terminal will again be positive on discharge. 

Exp. 27 : Fill the U tube with acidulated water and connect the 
voltameter, Fig. 99, to two bichromate cells. After passing the cur- 
rent for a short time, causing an evolution of gas, disconnect the bat- 
teries and connect the voltameter to a galvanometer. A deflection of 
the needle indicates that a current is now passing through the volta- 
meter in an opposite direction to the former battery current. 

109. Commercial Storage Batteries.— 

Exp. 28 : Place two lead strips in the U tube, Fig. 94, fill with 
acidulated water and connect the plates to a detector galvanometer. 
No deflection is noted. Now connect the plates to two bichromate 
cells (in series), and after passing a current for a short time examine 
the plates, and you will find that the positive plate has become 
brownish in color, while the negative plate is the same as before. 
Connect the plates to the galvanometer, and note that the needle in- 
dicates the discharging current. 

Lead plates in dilute sulphuric acid were first used by 
Plante, from whom this type of cell takes its name. The 



ELECTROLYSIS. 



85 



action in charging such a cell is as follows : Electrolysis of 
water liberates oxygen on one plate (the positive) which 
combines with the lead to form lead peroxide (Pb0 2 ), while 
hydrogen accumulates on the other plate (the negative). On 
discharging the cell the oxygen of the peroxide plate com- 
bines with the hydrogen of 
the liquid, liberating oxygen, 
which, in turn, combines 
with the hydrogen of an 
adjacent molecule, until 
finally the hydrogen on the 
other plate is reached. Com- 
mercial storage batteries are 
modifications of the above 
type. The E. M. F. of such 
a secondary cell is about 2.1 
volts. Fig. 96 illustrates the 
construction of an accumu- 
lator. 

The discharging current 
depends upon the area of 
the plates used, while the 
length of discharge depends 
upon the weight of the 
plates. To increase the rate 
of discharge, a number of 
plates are fastened to 




one 



Fig. 96.— Chloride Accumulator. 
Positive element, two plates; negative ele- 
ment, three plates. 

terminal forming the negative 
element, or grid, and one less than the number used form 
the positive element (the active plate). The plates are 
then dovetailed together, and prevented from touching -each 
other by the insertion of rubber bands or ebonite strips. The 
solution used is dilute sulphuric acid (about a 20 per cent, so- 
lution). The lead plates are sometimes perforated, and into 
the perforations of the positive plates is pressed red lead, 
while the negative perforations are rilled with finely divided 
particles of metallic lead. 

QUESTIONS. 

1. Xame all the effects of an electric current and give a commercial 
application of each. 

2. Explain the principle of an electric incandescent lamp. 

3. Why is it that the lead wires to a lamp do not get as hot as the 
circuit inside the glass bulb ? 



86 PRACTICAL ELECTRICITY. 

4. How would you classify liquids according to their conducting 
power, and the chemical effect of the current upon them ? 

5. What do you mean by electrolytic decomposition ? 

6. What is an electrolyte? 

7. What is electrolysis ? 

8. How would you find the polarity of an electric light circuit with 
a tumbler of water? Give sketch. 

9. Define the terms anion, cathode, anode, cathion. 

10. What is a voltameter ? Give sketch. 

11. Give the action in the copper voltameter, also a sketch. 

12. Give two reasons for inferring that current has direction. 

13. What is the action in a copper voltameter when a platinum 
plate is substituted for a copper plate ? Give sketch. 

14. State briefly your idea of the art of electroplating. 

15. What effect upon an electrolytic deposit will be noted when too 
strong a current is used ? 

16. How does electrotyping differ from electroplating? 

17. What is a polarity indicator, and how is it used ? 

18. What is an accumulator ? 

19. How does a storage battery differ from a primary battery ? 

20. What does a storage battery store ? 

21. Explain the action in a simple type of storage battery. Give 
sketch. 

22. What is meant by the terms charging and discharging? 

23. How would you connect a storage battery to a circuit to be 
charged ? Show by a sketch the polarity of the cell and the polarity 
of the charging line. 

24. Describe fully a commercial type of storage battery. State the 
actions on charge and discharge. Give sketch. 

25. When is a storage battery discharged ? 



LESSON XI. 

MEASUREMENT OF CURRENT STRENGTH. 

Strength of Current — Variation of Current and Current's Effects — 
How the Effects Vary with the Current Strength — Variation of 
Effects with the Same Current Strength Through Dissimilar Ap- 
paratus — Measurement of Current Strength — Definition of the 
Unit of Current Strength— Definition of a Unit Quantity of Cur- 
rent — The Ampere-Hour — Weight Voltameters— Voltameter Cal- 
culations — Construction of the Gas Voltameter — Directions for 
Using the Gas Voltameter — Measuring Current Strength by a Gas 
Voltameter — Current Strength Used in Electroplating and in 
Commercial Apparatus— Questions and Problems. 

110. Strength of Current. — Either the magnetic, heat- 
ing, or chemical effect of an electric current may be employed 
to determine whether a current is flowing through a wire. If 
the magnetic effect of a current flowing through a wire 
is greater than that of another current, the intensity of the 
current, or the strength of the current, must be greater, since 
the magnitude of any of the current's effects varies with the 
current assumed to be flowing. We express the rate of flow 
of water through a pipe as so many gallons per second, which 
expression includes a definite quantity of water and a unit of 
time ; that is, at a rate of flow of one gallon per second, we 
mean that one gallon passes any point in the pipe once every 
second. By the strength of an electric current we mean the 
rate of transfer of electricity past any point in the circuit in a 
unit of time (the second). It is obvious that the magnitude 
of the effects of the current may be used to measure the 
strength of the current, 

111. Variation of Current and Current's Effects. — 

Exp. 29 : Pass a current under a force of one volt through a coarse 
wire galvanometer and note the deflection. Repeat the experiment 
with twice the applied pressure, two volts, and the deflection of the 
magnetic needle is less than twice as much as before, although the 
force is doubled and the current strength, varying as the force, must also 
have been doubled. 

Exp. 30 : With an applied pressure of 4 volts note the amount of 
gas generated from dilute sulphuric acid in 2 minutes by the appara- 

87 



88 PRACTICAL ELECTRICITY. 

tus in Fig. 99. Repeat the experiment with 8 volts and note that in 
the game time twice the volume of gas is generated. 

Exp. 31 : Using copper sulphate and two copper plates, carefully 
weighed before the test, apply a force of 2 volts for 10 minutes and 
then re-weigh the plates. The negative plate has gained in weight 
exactly what the positive plate lost. Repeat the experiment with 4 
volts for the same length of time and the weight is increased' to 
double what it was before. 

Exp. 32 : Coil a number of turns of No. 30 iron wire around the 
bulb of a thermometer, and place it in a small test tube containing a 
measured quantity of water. Place the test tube in a larger vessel 
containing sawdust to prevent heat radiation. Apply a force of 4 
volts for 10 minutes and by aid of the thermometer note the rise in 
the temperature of the water. Repeat the experiment with 8 volts 
for the same period of time, with the same quantity of water, and at 
the previous starting temperature. Neglecting the heat lost by radia- 
tion, the increase of temperature is nearly four times as great as in the 
first test, although the current was only doubled. If- the current had 
been tripled, the temperature rise would have been 9 degrees, and 
with the current quadrupled the rise would have been 16 degrees, 
and so on. 

112. How the Effects Vary with the Current Strength. 

The above experiments may be made simultaneously when 
the circuit is arranged, as in Fig. 97, in which nearly all the 
effects of the current are represented. The circuit is made up 
as follows : starting from the positive battery terminal the cur- 
rent would flow (1) through a few turns of coarse wire in 
the galvanometer coil; (2) a large number of turns of 
coarse wire on the spools of the electromagnet; (3) a dilute 
solution of sulphuric acid in the mixed gas voltameter, the 
current to pass between platinum electrodes ; (4) a solu- 
tion of copper sulphate, the current to pass between copper 
electrodes ; (5) a number of turns of No. 30 iron wire 
wound around the bulb of a thermometer and immersed in a 
vessel of water placed in sawdust; (6) through the carbon 
filament of an incandescent lamp; (7) through a switch to 
the negative pole of the battery, and (8) from the negative 
pole of the battery through it to the positive pole. 

When the switch is closed, the current produces the follow- 
ing effects simultaneously : The magnetic needle is deflected ; 
it requires a certain number of pounds pull to detach the 
keeper from the electromagnet; hydrogen and oxygen gas 
rise in the graduated test tube, displacing the acidulated 
water therein ; metallic copper is deposed from the copper 
positive plate and deposited upon the copper negative plate, 
so that it thereby gains in weight ; heat is evolved in the 



MEASUREMENT OF CURRENT STRENGTH. 89 



vessel containing the iron coil of wire; very dim light is 
given by the incandescent lamp ; zinc is being decomposed in 
the batteries furnishing the electrical energy to produce all 
these effects outside of the battery. 

All the effects are produced the instant the switch is closed, 
but only four can be noted instantly — the needle's deflection, 
the attractive force of the magnet, the evolution of gas, and 
the brilliancy of the lamp. The weight of copper deposited, gas 
liberated, and the number of degrees rise in temperature, due 
to a current flowing for only an instant is so small as to be 
practically immeasurable. By allowing the current to flow 
for a certain period of time a measurable quantity is obtained, 
which divided by the time in seconds gives the magnitude of 
the effect per second, or the current strength. Keep the 
switch closed for about five minutes (5 X 60= 300 seconds), 
then by dividing the volume of gas generated in 300 seconds 
by 300 we obtain the gas generated per second, and simi- 
larly with the gain in temperature and the gain in weight of 
the negative copper plate. 



ssss 




(Stfflt/Mvy/AAAAA*^ 



J*nMUV*&s*+jO€*JC/ Umfv 



Fig. 97. — The Effects of the Current and their Variation with a Variation in 
Current Strength. 

This is a simple series circuit and the current is the same in all parts of it. 



90 PRACTICAL ELECTRICITY. 

We thus get a series of results of the different effects, all 
corresponding to the same strength of an electric current, 
flowing for a unit of time. The intensity of current that de- 
flected the needle in one part of the circuit, or magnetised the 
iron core of the electromagnet, is exactly the same as that 
which decomposed the acidulated water or the copper sul- 
phate, or heated the iron wire. This is a simple series circuit, 
although made up of a number of different conductors, and the 
current is the same in all parts of a series circuit ; that is, the 
rate of flow past any point selected is the same. The order 
of the arrangement of the apparatus is also immaterial. By 
increasing the E. M. F. of our battery so that twice the pres- 
sure is applied to this same circuit, we double the current 
strength or rate of flow. The switch is closed for the same 
time as before, and the results noted for comparison. A third 
test may also be made, using three times the force. The 
record of three such tests, with apparatus as arranged in Fig. 
97, is as follows : 

Tests of Current's Effects. 

Testl. Test 2. Test 3. 

Galvanometer, deflections 25 37 42 

Electromagnet, pounds pull 54 65 70 

Gas voltameter, volume of gas generated per 

second 17 .34 .51 

Copper voltameter, gain in weight per second .0003 .0006 .0009 

Calorimeter, degrees rise per second .... .1 .4 .9 

Incandescent lamp, candle-power 5 8 12 

From the above tests the following facts will be noted : The 
deflection of the galvanometer needle is not directly propor- 
tional to the current, doubling the current, not doubling the 
deflection. The number of pounds pull, or attractive force, 
is not directly % proportional to the current strength. The 
volume of gas generated is exactly proportional to the cur- 
rent, and if the current had been quadrupled the gas gener- 
ated per second would have been four times as great, and so 
on. The deposit of copper is directly proportional to the 
current, doubling the current, also doubling the gain in 
weight. The rise in temperature was not doubled, but in- 
creased four-fold ; with three times the current strength the 
rise is nine-fold, the temperature rise thus increases di- 
rectly as the square of the current strength ; for example, 1 
unit of current produces 1 degree rise; 2 units, 4 degrees 



MEASUREMENT OF CURRENT STRENGTH. 91 

rise ; 3 units, 9 degrees rise, etc. ; the lamp's luminosity is 
not directly proportional to the current. 

113. Variation of Effects with the Same Current 
Strength Through Dissimilar Apparatus. — If the series 
circuit, Fig. 97, had contained two pieces of each apparatus of 
widely varying dimensions of plates, convolutions in the coils, 
size of wire, etc. , what would have been the result ? The cur- 
rent strength would have been the same in each part of the cir- 
cuit as before. The tine wire galvanometer would produce a 
larger deflection than one of a few turns of the same diame- 
ter. The electromagnet, with the greater number of turns, 
would have the greater attracting power. A gas voltameter 
with small plates, widely separated, would evolve the same 
volume of gas as a voltameter with much larger plates placed 
close together, since the gas evolved is proportional to the 
rate of flow of electricity, which is the same through both 
instruments, and hence independent of the size of the elec- 
trodes or their distance apart. Similarly, in two copper vol- 
tameters in the same series circuit, the weight of copper 
deposited is independent of the size of the plates or their 
distance apart, and would be the same for each voltameter, 
however constructed. More heat would be generated by the 
coil of many turns of fine wire. The current flowing through 
a circuit is the same in all parts of that circuit ; thus, if at 
two different points in a circuit a gas voltameter be inserted, 
the gas evolved at the one point will be exactly equal to 
that evolved at the other point. 

114. Measurement of Current Strength. — To compare 
different strengths of current some arbitrary standard must 
be adopted. If we defined our unit of current strength as 
such a rate that flowing every second would deflect our mag- 
netic needle, ^f 112, 25 degrees, we would also have to 
specify the length of needle, diameter of coil, number of 
turns, place where the needle was set up, etc., which would 
make it an impractical standard. Also in the case of the 
electromagnet, all the dimensions and quality of the iron, 
the keeper and the wire, etc., would have to be stipulated. 
If we Avould express the unit of current strength as such a 
rate of flow that would attract a keeper with 54 pounds, then, 
again 2 units of current do not attract the keeper 108 pounds, 
as might be expected, but only 65 pounds. (See test, ^[112.) 
The current strength is directly proportional, however, to the 



92 PRACTICAL ELECTRICITY. 

amount of gas generated per second or the amount of metal 
deposited per second, so that of all the effects the chemical 
one is the best adapted for furnishing a standard unit of cur- 
rent strength, since such a standard will be independent of 
the apparatus used to produce the effect. The heating and 
magnetic effects are employed in various practical instru- 
ments for measurements, but they are standardized by the 
chemical effect. 

115. Definition of the Unit of Current Strength. — 
The strength of current is directly proportional to the amount of 
chemical decomposition it can produce in a given time, and as a 
steady current passed through a solution of nitrate of silver in 
water, in a silver voltameter, deposits silver at the rate of 
0.001118 grams per second, this value is taken as a unit of cur- 
rent strength and called one ampere.* 

One ampere will deposit in one second : 

. 0003286 grams of copper in a copper voltameter ; 
.0003386 grams of zinc in a zinc voltameter. 
One ampere will also decompose .00009326 grams of dilute' 
sulphuric acid per second. One ampere will also evolve 
.1733 cubic centimeters of mixed gas per second in a gas 
voltameter (when the temperature is 0° Centigrade and the 
atmospheric pressure 76 centimeters of mercury). 

116. Definition of a Unit Quantity of Current.— Dis - 
tinction must be made between the total quantity of electricity 
that passes through a circuit in a given time, and the rate of 
flow of electricity during that time. For example, at the rate 
of flow of one gallon per second, 3600 gallons of water 
would be delivered to a tank in an hour, the total quantity 
being readily distinguished from the rate of flow. We might 
consider the gallon per second as a unit of quantity and name 
it, but this has not been done in hydraulics, although it is 
done in the case of electricity. The total quantity of water 
equals the rate multiplied by the time in seconds ; thus, at 
a rate of flow of 8 gallons per second, in 60 seconds, the 
total quantity delivered would be 480 gallons, which same 
quantity could be delivered to a tank in one second if the rate 
were 480 gallons per second, or in one-half second if the rate 
were 960 gallons per second, or in 480 seconds if the rate were 
only one gallon per second. Similarly the unit quantity of 

♦Values given by Ayr ton. 

One ounce = 28.34 grams. 



MEASUREMENT OF CURRENT STRENGTH. 93 

electricity is the amount of electricity that flows per second past any 
point in a circuit ivhen the current strength is one ampere, and 
this unit quantity has been called the coulomb. If a current 
strength of one ampere flows for 60 seconds, then the total 
quantity is 60 ampere-seconds, or 60 coulombs of electricity. 
First : To find the total quantity of electricity 

PASSING THROUGH A CIRCUIT IN A GIVEN TIME : 

Multiply the current strength {expressed in amperes) by the 
time {expressed in seconds). 

Let C — current strength in amperes ; 

Q — = the total quantity of electricity in coulombs ; 
t = time the current flows (in seconds) ; 
Then : 

Quantity = current strength X time, 
or coulombs = amperes X seconds, 
or substituting the above symbols, 

Q = CXt . . (1). 

Prob. 1 : An incandescent lamp requires a current of one-half an 
ampere to maintain its proper brilliancy. If the lamp is lighted two 
hours what quantity of electricity will be consumed? 

2 hours = 60 X 60 X 2 = 7200 seconds. 

By Formula ( 1 ) Q = C X t = J X 7200 = 3600 coulombs. 

C = ^ ampere, t = 7200 seconds. 

Second : To find the average current strength (in 

amperes) when the time the current flows, and the 

quantity of electricity are known : 

Divide the quantity (in coulombs) by the time (in seconds). 

Current strength = Quantity -*- time, 

or Amperes = Coulombs -*- Seconds, 

. Coulombs 

or Amperes == = — , 

beconds 

or by substitution C = — . . .(2). 

x 

Prob. 2 : What is the average rate of current strength in a lamp 
circuit if the electrical consumption was 54000 coulombs and the cur- 
rent used for 5 hours ? 

5 hours = 60 X 60 X 5 = 18000 seconds. 

By Formula (2 ) C = j = ^^ = 3 amperes. 

Q = 54000 coulomb?, t = 18000 seconds. 

Third : To find the time (in seconds) required for a 

GIVEN QUANTITY OF ELECTRICITY (iN COULOMBS) TO PASS A 

point in a circuit : 



94 PRACTICAL ELECTRICITY. 

Divide the quantity of electricity (in coulombs) by the rate of 

flow (in amperes). 

T . Quantity 

~~ Current Strength' 

~ , Coulombs 

or beconds = -. , 

Amperes 

or by substitution t==^ (3). 

\j 

Prob! 3 : How long a time, will be required to pass 18000 coulombs 
through an electroplating bath if the average rate of current strength 
is 6 amperes ? 

By formula (3) t= ~ = — a — =3000 seconds, or — — = 50 minutes. 
Q = 18000 coulombs, C = 6 amperes. 

117. The Ampere-Hour. — The coulomb is- a very small 
unit of quantity. A larger unit, the ampere-hour, is often 
used. One ampere-hour would be the quantity of electricity 
that would pass any point in a circuit in one hour, when the 
strength of current is one ampere. One ampere-hour 
obviously equals 2 amperes for one-half hour ; 4 amperes for 
one-quarter hour, or one-quarter ampere for 4 hours and so 
on. One ampere-hour also equals 3600 coulombs. 

The capacity of batteries is rated in ampere-hours. For 
example a 100 ampere-hour cell would mean one in which 
sufficient chemicals were present to maintain one ampere for 
100 hours ; 2 amperes, for 50 hours, etc. An ampere-hour 
recording meter is placed in a lamp circuit so that it will 
record the total quantity of electricity that has been utilized, 
or the total ampere-hours. 

To FIND THE AMPERE-HOURS CONSUMED BY ANY ELECTRICAL 
APPARATUS : 

Multiply the average strength of current (in amperes) by the time 
(expressed in hours) that the current has been maintained. 

Ampere-hours (quantity) = Amperes X hours; 

A Ampere-hours 

Amperes = — — r ; 

r hours. 

Hours = Ampere-hours 

Amperes. 

Prob. 3-A : A current of 6.5 amperes was maintained by a cell for 4 
hours. What quantity of electricity has been used? 



MEASUREMENT OF CURRENT STRENGTH. 95 



Quantity = amperes X hours = 6.5 X 4 = 26 ampere-hours. 
Suppose the cell has a capacity of 78 ampere-hours, how long could 
the above current be maintained ? 



Hours = Q^ntity 
Amperes 



_78 
6.5 



12 hours. 



118. Weight Voltameters. — Current strength may be 
determined by a weight voltameter, one in which the weight 
of metal deposited or 
weight of water decom- 
posed, serves to deter- 
mine the rate of flow ; 
or a gas voltameter in 
which the volume of 
mixed gas to be evolved 
is used to determine the 
current strength. A 
weight voltameter is 
illustrated in Fig. 98. 
The two outside plates 
form the anode, and are 
joined together and to 
one binding post, while 
the cathode is placed 
between them and con- 
nected to the other bind- 
ing post. The cathode 
thus receives a deposit 
on both sides. An adjustable arm serves to lower the 
plates into the electrolyte. A gas voltameter is described 
in % 120. 

119. Voltameter Calculations. — First : To calculate 

THE STRENGTH OF AN UNKNOWN CURRENT (iN AMPERES) WHICH 
HAS PASSED THROUGH A WEIGHT VOLTAMETER : 

Find the weight of metal deposited per second by dividing the 
total gain in weight by the time (in seconds) the current flows 
through the instrument ; divide this quotient by the weight depos- 
ited by one ampere in one second, and the result is the strength 
of current expressed in amperes. 

Let C = current strength in amperes ;* 
W = total gain in weight ; 

t = time in seconds current flows ; 
K = weight deposited by one ampere in one second. 




Fig. 98. 



-Construction of a Weight 
Voltameter. 



One cathode between two anodes. 



96 PRACTICAL ELECTRICITY. 

Substituting for the above statement then : 

. weight gained 

Amperes = — -. — ryir- > 

^ gain per ampere- sec. X time. 

« C = TT*t W- 

If W is expressed in grams : 

K for a copper voltameter is .0003286 gram ; 

K for a zinc voltameter is .0003386 gram ; 

K for a silver voltameter is .001118 gram; 

K for a sulphuric acid weight voltameter is .00009326 
gram ; 

K for a sulphuric acid gas voltameter is .1733 cubic cen- 
timeter. 

Prob. 4 : The negative plate of a copper voltameter has increased 
in weight by 1.818 grams in thirty minutes. What was the average 
rate of current strength ? 

W 1 818 

By Formula (4) '0—^ = 00 03286 X 1800 = 3 - 073 anl P ere8 ' 
K for copper is .0003286, t = 30 minutes = 30 X 60 = 1800 sec. 
Second : To find the weight of any metal that will 

BE DEPOSITED IN A VOLTAMETER BY A GIVEN CURRENT IN A 
GIVEN TIME : 

Multiply the current strength by the time {in seconds) and this 
product by the weight deposited by one ampere in one second (K), 
the result is the weight expressed in grams (one pound = 
453.59 grams). 

Weight (gained) = Current X time X K, 

or W = CxtxK (5). 

Prob. 5 : In an electroplating bath how many grams of zinc will 
be deposited by a current of 5 amperes in 45 minutes ? 

By Formula (5) ¥=CXtXK = 5X 2700 X .0003386 = 4.5711 
grams. 

K for zinc = .0003386. 
t = 45 minutes = 45 X 60 = 2700 seconds. 

Third : To find the time required to electrolytically 

DEPOSIT ANY GIVEN WEIGHT OF METAL WITH A GIVEN CURRENT 
STRENGTH : 

Divide the iveight by the current strength, and by the iveight 
deposited by one ampere in one second (K), the result is the 
time expressed in seconds. 



MEASUREMENT OF CURRENT STRENGTH. 97 



Time = Wei g ht (gain ed) 
Current X K ! 

or t (seconds) = 



CXK 



(6), 



Prob. 6 : How long a time will be required to deposit 5.9328 grams 
of silver on a copper-plated teaspoon with a current of 2 amperes ? 



By Formula (6) t 



W 



5.9328 



2 X .001118 



2653 seconds, or 



2653 
60 



CXK 

= 44 minutes 13 seconds. 
K for silver = .001118 gram. 

120. Construction of the Gas Voltameter. — The gas 

voltameter is convenient for individual laboratory use with a 
large body of students, as it obviates the necessity of a pair 
of scales for each student. A demonstration type of instru- 
ment is shown in Fig. 100. A student' s ^ — ^ 
voltameter is illustrated in Fig. 99, and ( J 
is composed as follows : pfl|l* 

1 brass stand (16 inches high) 

1 glass U tube 

2 platinum electrodes sealed in a glass tube 
and connected by a copper wire, to which 
connectors are attached 

2 rubber corks for electrodes 

1 glass burette, graduated from to 30 
cubic centimeters and reading in tenths of a 
cubic centimeter 

2 adjustable clamps 
8 inches rubber tubing 
2 brass connectors 
1 pinch cock, for use when it is used as an 

electrolytic cell for copper, etc. 

121. Directions for Using the Gas 
Voltameter.— 

(1) Attach both clamps to the stand. (2) 
Attach one end of the rubber tube to the 
glass U tube and carefully clamp it by the 
lower clamp on to the stand. (3) Attach 
the other end of the rubber tube to the 
burette and carefully clamp it by the upper 
clamp. (4) Adjust the position of both 
clamps so that the* zero position of the 
burette is about one-half inch below the 
level of the top of the U tube. (5) Pour the acidulated water into 
the mouth of the burette till the water in the U tube is about one- 
half inch from the top, the height of liquid in the burette should be 
on a level with or above the zero mark. (6) With the electrodes 
7 




Fig. 99.— Student's Sul- 
phuric Acid Gas 
Voltameter. 



98 PRACTICAL ELECTRICITY. 

inserted through the corks, place each one in position, carefully, by 
giving a slight twist to the right as the cork enters. (7) The water 
level in the U tube and burette should now be the same, or further 
adjustment must be made to attain this result. The level in the 
burette does not necessarily have to correspond with the zero gradua- 
tion, but must not be below it. (8) Unclamp the burette and hold 
it nearly horizontal. The liquid will not run out if the corks are 
tight, so that this is the air leakage test. (9) Attach the connectors 
arid wires from the source of E. M. F. (which should be 2 or more 
volts) having a final switch in the circuit. 

In electrolyzing any substance a back or contrary E. M. F. 
is set up in opposition to the decomposing current, due to the 
chemical affinity of the substances olis-united, which tend to 
re-unite. Sufficient force must therefore be applied to over- 
come this force of chemical affinity. For example, in the 
case of water this opposing force is about 1.5 volts, so that it 
requires a greater force than 1.5 volts to electrolyze water, 
hence our two cells are joined in series. 

Exp. 33 : Close the switch connecting the above voltameter in cir- 
cuit. Bubbles of gas rise in the U tube from both electrodes, displace 
the water and force it up the burette. Twice the volume of gas 
(hydrogen) is collected over the negative electrode that is collected 
over the positive electrode (oxygen). Run the test till the volume of 
hydrogen gas occupies nearly the whole limb of the U tube when the 
switch should be opened. 

Exp. 34 : With the gases collected in Exp. 33, lower the burette as 
far as possible (to decrease the hydrostatic head). Remove the cork 
for an instant from the hydrogen limb and quickly apply a lighted 
match. The hydrogen burns with a pale bluish flame. Replace the 
cork quickly so that the solution is not forced out of the U tube. Now 
remove the cork from the oxygen, extinguish the flame of the match 
and quickly apply the glowing spark to the oxygen ; the match im- 
mediately bursts into a flame again. Replace the cork quickly. Oxygen 
gas does not burn, but supports combustion. If both gases are col- 
lected in a single tube, as in the form of the voltameter used in Fig. 
97, when a lighted match is presented to the mouth of this tube the 
hydrogen, instead of burning, explodes with a violent report, due to 
the presence of the oxygen. 

122. Measuring Current Strength by a Gas Volta- 
meter. — First : To find the current strength when a 

VOLUME OF GAS IS EVOLVED IN A GIVEN TIME : 

Divide the volume of gas evolved by the time (in seconds) and 
this quotient by the volume of gas evolved by one ampere in one 
second (K). The result is the current in amperes (subject to 
corrections when greater accuracy is required).* 

* Neglecting temperature, barometric pressure and hydrostatic head. 



MEASUREMENT OF CURRENT STRENGTH. 99 

_ volume of gas generated 

current — — — ; - ^ — r ^ — > 

time (seconds) X K 

' 0rC = t^K W- 

K for the mixed gases or the two gases evolved separately = 
.1733 c. c. (^ 115). 
Second : The volume of gas (in cubic centimeters) which 
will be evolved by a given current in a given time is 

volume evolved (c. c. ) = current X time (seconds) X K, 

orV = CXtxK (8). 

Third : Also the time required to evolve a certain quan- 
tity of gas with a given current is 

, N volume 

time (seconds) = ~ , w T , y 

v J Current X K 

Exp. 35 : Set up the gas voltameter again according to the direc- 
tions in \ 121. To correct error caused by the decrease in volume of 
the gases, due to the weight of the liquid in the burette at the end of 
the test, lower the burette before the test so that the height of 
liquid in it is about on a level with the bottom of the U tube. Secure 
a watch (preferably with a second hand). Note the level of the 
liquid on the burette scale before starting the test. Close the switch, 
noting the exact time. Allow the gas to be evolved till either the 
hydrogen limb of U tube is nearly full, or the liquid in the burette 
approaches the end of the scale. Bo not run above scale limit. Note 
the time of opening the switch, also the height of the liquid in the 
burette. 

Prob. 7: The following data is recorded in Exp. 35. Find the 
strength of current. 

Level in burette before test 2.6 c. c. 

Level in burette after test 28.8 c. c. 

Volume of gas evolved = 28.8 — 2.6 = 26.2 c. c. 

Time of closing switch 8.40 — 15. 

Time of opening switch 8.45 — 15. 

Length of run = 5 minutes = 5 X 60 = 300 seconds. 

26 2 
Total ga? generated per second = — ^ = .0873 c. c. 

oOO 

One ampere in one second (one coulomb) generates .1733 cubic 

centimeters of gas per second, therefore ' Q = .5 ampere, 

V 26 2 

or by Formula (7) C = ^ = m3 x m = .5 ampere. 

L.ofC. 



100 



PRACTICAL ELECTRICITY. 




When more accurate calculations are desired the following formula 
is used to find the current strength : 

V X h X 273 
.1733 X 76 (273 +C°) X t v J ' 

V = volume of gas in c. c. 
h = height of barometer in centimeters. 
C°= temperature of room, Centigrade, 
where test is made, 
t = time (in seconds) gas is evolved. 

Prob. 8 : In an experiment the volume 
of gas generated in a gas voltameter was 
found to be 20 cubic centimeters in 50 
seconds, its temperature (t'aken as the tem- 
perature of the room) was 20 degrees, 
Centigrade scale, the pressure of the atmos- 
phere was equal to 75 centimeters of mer- 
cury. What was the current strength ? 
Bv Formula (10) 

r 20 X 75 X 2 73 

U — .1733 X76 (273 + 20) X 50 

= 2.12 amperes. 
To find the volume of gas generated by a 
known current : 

„ _ .1733xCx76 (2 73 + C°)Xt n . , 
V — hX273 ' ' UiJ ' 

Prob. 9 : What volume of gas would be 
produced in a gas voltameter in 30 seconds 
by a steady current of 18 amperes, supposing the temperature of the 
gas so produced is 20 degrees C. and the barometer stands at 77.5 
centimeters? 

t, t? i /-.-.n tt .1733x18X76(273 + 20) X 30 

By Formula (11) V = 77 5 v 2^3 = 98.49 c. c. 

123. Current Strength Used in Electroplating. — If the 

metallic deposition is performed too rapidly the deposit be- 
comes open and of a powdery appearance. A low current 
density produces a hard, close grained surface. The usual 
densities used in practice are : 

Copper acid bath, 5 to 10 amperes per square foot of area to be plated. 
Copper cyanide bath, 3 to 5 amperes per square foot of area to be 

plated. 
Nickel, double sulphate, 6 to 8 amperes per square foot of area to be 

plated. 
Gold, chloride in cyanide, 1 to 2 amperes per square foot of area to be 

plated. 
Silver, double cyanide, 2 to 5 amperes per square foot of area to be 

plated. 



Lattery 

Fig. 100.— Gas Voltameter. 
Hoffman's Lecture Room Form. 



MEASUREMENT OF CURRENT STRENGTH. 101 

Prob. 10 : A piece of sheet-iron, six inches square, is to be plated 
on both sides in a copper acid bath. What current strength is 
required ? 

From If 123 : Current density for copper cyanide bath is 5 to 10 am- 
peres per square foot — 

Say 8 amperes, 144 square inches = 1 square foot. 

Area of plate (both sides) = 6 X 6 = 36 square inches X 2 = 72 
square inches. 

72 
774 = . 5 square foot at 8 amperes per square foot = 4 amperes. 

Table IV.— Value of Current Strengths Used in Practice. 

The strength of current required to operate a 110 volt, 16 candle-power, 

incandescent lamp is about 0.5 ampere 

For an enclosed 110 volt arc lamp 5 amperes 

For an open-air arc lamp 8 to 10 amperes 

For a trolley car equipped with two 25 horse power 

motors when fully loaded 75 amperes 

For a 110 volt fan motor % to 2 amperes 

For the average electric bell yo ampere 

For the average telegraphic circuit 025 ampere 

For 110 volt Weston voltmeter, full scale deflection . . .0006 ampere 
For electrical welding 20 to 50,000 amperes 

QUESTIONS. 

1. What do you understand by current strength ? 

2. State some experiments you would make to ascertain how the 
effect of a current varies with its strength. 

3. Which effects of the current are directly proportional to it ? 

4. Which effects do not vary directly with the current strength? 

5. An electromagnet attracts its keeper with a force of 18 pounds. 
If twice the E. M. F. be applied to the magnet coils, what will be the 
comparative result? 

6. A coil of iron wire carrying a current is thrown into a tumbler 
of water for 10 minutes and the temperature is changed 6 degrees. 
The current is now exactly doubled for the same length of time. 
What is the change in temperature ? 

7. Which is the most suitable effect of the current by which it can 
be measured? Give reason for your answer. 

8. What would be the objection to considering the standard unit 
of current strength, as of such a strength that would deflect a galvan- 
ometer needle 30 degrees ?- 

9. A current strength is said to be 5 amperes. What do you un- 
derstand by this expression ? 

10. What is the unit of current strength ? Give example. 

11. Explain the difference between the terms " current strength" 
and "quantity of electricity." 

12. What is the unit of electrical quantity ? 

13. Five coulombs are used every second by a lamp. What is the 
current strength ? 



102 PRACTICAL ELECTRICITY. 

14. Why is it that you cannot electrolyze water with one Daniell 
cell? 

15. Platinum and copper plates are dipped into a solution of zinc 
sulphate and a current passed from the platinum to the copper plate. 
How are the plates affected ? 

16. Give an example of chemical composition and deposition in the 
same circuit. 

17. Copper and platinum plates are dipped into copper sulphate. 
What is the action when the current is passed from the copper to the 
platinum plate ? 

PROBLEMS. 

1. How many ampere-hours will be recorded by a meter through 
which 160 amperes has passed for three-quarters of an hour? Arts. 
120 ampere-hours. 

2. A 100 ampere-hour Edison-Lalande cell is discharged through 
an electromagnet at a 2\ ampere rate. How long will the cell main- 
tain this current through the magnet? Ans. 40 hours. 

3. A meter records 500 ampere-hours. It was in circuit 5 days for 
10 hours each day. What was the average rate of current used ? Ans. 

10 amperes. 

4. How many coulombs have passed through an arc lamp in 
three-quarters of an hour if the current was 10 amperes ? Ans. 27,000 
coulombs. 

5. What current strength is required to deposit 5 grams of copper 
upon an iron spoon in 35 minutes? Ans. 7.8 amperes. 

6. A meter records 54,000 coulombs in 3 hours. What was the 
average strength of current? Ans. 5 amperes. 

7. How many grams of copper will be deposited on an iron plate 
used for a ship's hull in 10 hours if the average strength of current 
is 25 amperes ? Ans. 295. 74 grams. 

8. The two terminals of an electric light circuit are dipped into a 
tumbler containing 5 grams of acidulated water. How long would a 
current of 3 amperes flow before the water was entirely decomposed? 
Arts. 4 hours 57 min. 51 sec. 

9. Using a current density of 5 amperes per square foot, how long a 
time is required to copper plate both sides of a square iron plate meas- 
uring 4 feet on a side, supposing sufficient thickness is attained when 
the coating weighs 4 grams per square foot ? Ans. 40 min. 33 sec. 

10. An inverted test tube, capacity 40 c. c, is filled with acidulated 
water, and the terminals, of several cells in series, are introduced un- 
derneath the tube. In 5 minutes half of the tube was filled by gas. 
What was the strength of current in the circuit? Ans. 0.384 ampere. 

11. The negative zinc plate of an Edison electrolytic meter increased 
in weight during a certain time, 3.445 grams. This amount represents 
one one-thousandth part of the current used by the consumer. With 
how many ampere-hours should he be charged ? Ans. 2834 ampere- 
hours. 

12. What bill would you render for the current consumed in Prob. 

11 if the station's rate was 1.5 cents per ampere-hour. Ans. $42.51. 



LESSON XII. 
RESISTANCE. 

Resistance — Table V. Conductors and Insulators — The Unit of Re- 
sistance — Laws of Resistance — Table VI. Resistance of a Mil- 
Foot of the Metals -Calculation of Resistance — Wire Measure — 
The Circular Mil— The Square Mil— The Wire Gauge— Table 
VII. B. &S. Wire Gauge— Table of Conductivity and Resistivity 
of Metals— Internal Resistance of a Battery — Questions and 
Problems. 

124. Resistance. — All bodies offer some opposition to the 
passage of an electric current through them. Pipes offer 
opposition to the flow of water through them, due to the 
friction between the running water and the sides of the 
pipes. 

Electrical resistance is the opposition offered by any substance 
to the flow of an electric current through it. No conducting 
body possesses perfect conductivity, but every conductor 
offers some resistance to the passage of a current. All bodies 
conduct differently, some offering more opposition to the flow 
of current than others. If the opposition is small, the con- 
ductivity is good, and the body is classed as a conductor. 
When the opposition (resistance) is high, the conductivity is 
poor, and the substance is classed as a poor conductor, which 
ranks it as a good insulator. The property of an insulator is 
to obstruct the flow of current. With a good conductor for 
conducting current, and a good insulator for confining it to 
the conductor, we have the practical conditions for handling 
electricity. The metals and alloys are good conductors. 
Resistance is the reciprocal of conductivity. The greater the 
conductivity of a body the less its resistance ; the one de- 
creases in the same ratio as the other increases. Conductivity 
(the property of conducting) is sometimes called conductance. 
Resistance is sometimes called 



Exp. 36 : Connect spool 1 of the resistance spool set, Fig. 101, to 
a student's Daniell cell with the detector galvanometer, Fig. 153, in 
circuit, and note the deflection of the needle. 

103 



104 



PRACTICAL ELECTRICITY. 



NO. 1. 

This spool is wound with 

25 ft. of No. 24 B. & S. 
Copper Wire. 

Diameter, .0201 inoh 
Circular mil area (d 2 )= 

.0201 x 0201=404 CM. 
Ohms per 1000 feet=25.695 
Feet per ohm =38.918 

Ohms per pound =21.050 
Pure Copper Wire, Specific 
Gravity i 
Resistance at 
75° F. 



NO. 2. 

This spool is wound with 

50 ft. of No. 24 B. & S. 
Copper Wire. 

Diameter, .0201 inch 
Circular mil area (d 2 )= 

.0201 x 0201=404 C. M. 
Ohms per 1000 feet=25.695 
Feet per ohm =38.918 

Ohms per pound =21.050 
Pure Copper Wire, Specific 
Gravity 8.9. 
Resistance at 
75° F. 



NO. 3. 

This spool is wound with 

25 ft. of No. 18B.&S. 
Copper Wire. 

Diameter, .0403 inch 
Circular mil area (d 2 )= 

•0403x.0403=1624 C. M. 
Ohms per 1000 feet= 6.3911 
Feet per ohm =156.47 

Ohms per pound = 1.3023 
Pure Copper Wire, Specific 
Gravity 8.9. 
Resistance at 
75° F. 



NO. 4. 

This spool is wound with 

25 ft. of No. 24 B. & S. 

German Silver Wire. 

Diameter, .0201 inch 
Circular mil area (d 2 ) = 

.0201 x. 0201 =404 C. M. 
Ohms per 1000 feet=480.834 
Feet per ohm = 2 -°0o 

Ohms per pound =393.93 



Fig. 101.— Resistance Spool Set. 



Exp. 37 : Connect spool 2 in place of 
1, and note the deflection, which is 
smaller than before. Whv ? 

Exp. 38 : Connect spool 3 in place of 2, 
and note the deflection. It is greater 
than either 1 or 2. Why is this so,, since 
it is of the same length and material as 1 ? 

Exp. 39 : Substitute spool 4 for 3, and 
note the deflection. This is smaller than 
in any of the other cases. Spool 4 is of 
exactly the same length and cross- 
sectional area as spool 1. Why is the 
deflection so much smaller ? 

Exp. 40 : Connect several bichromate 
cells in series with spool 4, and pass a 
current through it for a short time. The 
spool becomes warm. Now connect it 
again in the same circuit as in Exp. 39, 
and note that the deflection is smaller 
than before. Why is this so, since it is 
exactly the same length, area, and material 
as in Exp. 39 ? 

125. Conductors and Insula- 
tors. — In the following table the 
substances are arranged in the order 
of their conductance, the best con- 
ductors being at the top, and the 
best insulators at the bottom of the 
list. Any subs tance in the table is 
approximately a better conductor than 
any substance which follows it ; thus, 
lead is a better conductor than 
mercury, but not so good as zinc. 
A slight variation in the quality of 
a substance would change its position 
in the list with reference to some 
other substance ; for example, some 
marble is useless for switchboards on 
account of metallic veins running 
through it. The same is true 
of slate, so that 
the position of 
these substances on 
the list is approxi- 
mate. 




RESISTANCE. 



105 



Good Conductors 

(metals and 

alloys). 



Table V.— Conductors and Insulators. 



f Silver 

Copper 
I Aluminum 
j Zinc 

Brass (according to composition) 

Platinum 

Iron 
j Nickel 

Tin 

Lead 

German silver (copper 2 parts, zinc 1, nickel 1) 

Platinoid (German silver 49 parts, tungsten 1 
part) 

Antimony 

Mercury 

Bismuth. 



Fair Conductors. 



Partial Conduc- 
tors. 



Non- Conductors or 
Insulators. 



Charcoal and coke 
Carbon 
Plumbago 
Acid solutions 
Sea water 
Saline solutions 
Metallic ores 

Living vegetable substances 
[ Moist earth. 

Water 

The body 

Flame 

Linen 

Cotton 

Mahogany 

Pine 

Kosewood 

Lignum vitse 

Teak 

Marble. 



Slate 

Oils 

Porcelain 

Dry leather 

Dry paper 

Wool 

Silk 

Sealing wax 

Sulphur 

Resin 

Gutta percha 

Shellac 

Ebonite 



Dry Woods. 



( Continued on page 106. ) 



106 PRACTICAL ELECTRICITY. 



Mica 
Jet 



Non-Conductors or J Amber 



Insulators. j Paraffin wax 

Glass (varies with quality) 
Dry air. 



I 



126. The Unit of Resistance. — The unit of resistance is 
called the Ohm, and is the resistance that would be offered to 
the flow of an electric current by a column of mercury 106 
centimeters (or 41.7322 inches) high, having a cross- sectional 
area of 1 square millimeter (or .00155 square inch) at 0° 
Centigrade (or 32° Fahrenheit). This is the Legal Ohm. 
In practice the value of the ohm, corresponding to the above 
standard, is as follows, approximately : 

1 ohm= 1000 feet of copper wire j* inch diameter (No. 
10 B. &S.). 

1 ohm = 250 feet of copper wire ^n inch diameter (No. 
16 B. &S.). 

1 ohm = 2 pounds of copper wire ^ inch diameter (No. 

16 B. & S.) or (250 feet per pound). 

15 
1000 feet of copper wire nearly 09 inch diameter (0000 

B. &S.) =.04967 ohm. 

3 

1000 feet of copper wire ^ inch diameter (40 B. & S. ) = 

1063 ohms. 

In calculating or measuring very low resistances one-mil- 
lionth of the value of an ohm is sometimes used and called 
the microhm. 

To express a resistance in microhms multiply by 1,000,000 or 

Microhms = ohms X 1,000,000 (12). 

_. microhms /10N 

0hms = 1,000,000 (13) - 

In measuring very high resistances one million ohms are 
used as the unit and called a megohm (often abbreviated meg.). 

Megohms ^j-^qq (14). 

Ohms = megohmsX 1,000,000 . .... .(15). 



• RESISTANCE. 107 

Prob. 11 : What is the equivalent resistance in megohms of 
47,500,000 ohms? 

-o T7 i ma\ 47,500,000 ,_ _ , 

By Formula (14) i qqq qqq = 47 - 5 megohms. 

Prob. 12: Give the equivalent resistance in microhms of .00385 
ohm. 

By Formula (12) .00385 X 1,000,000 = 3850 microhms. 
Prob. 13 : What is the equivalent resistance in ohms of 225 
microhms ? 

295 
By Formula (13) 1 QQ q quo = -000225 ohm. 

127. Laws of Resistance. — From the experiments made 
with the resistance spool set, ^[124, the following laws are 
deduced : 

I. It is the mass or weight (cross-sectional area) of a material 
which conducts and not its surface. This can be proved by 
using a wire tube in comparison with a sold wire of the same 
diameter in the experiments in ^[ 124. Law I, Fig. 102. 

II. The resistance of a conductor is directly proportional to its 
length. 2,000 feet of copper wire . 1 inch diameter will have 2 
ohms resistance ; 10,000 feet, 10 ohms, etc. Law II, Fig. 102. 

III. The resistance of a conductor is inversely proportional to its 
cross-sectional area, and in the case of round wire inversely pro- 
portional to the square of the diameter. Area varies inversely as 

the diameter squared, or area varies as j? 2 (see note below). 

A wire one-half inch in diameter has four times as great a 
resistance as a wire one inch in diameter, because as the area 
increases the resistance decreases. For example : No. 24 
(B. & S.) wire has a diameter of .02 inch, and No. 30 has a 
diameter of .01 inch, or one-half the diameter of No. 24 ; 39 
feet of No. 24 has a resistance of one ohm, and 9.75 feet of 

39 39 

No. 30 equals one ohm (which is nearly — = — = 9.75). 

Law III, Fig. 102. 

The area of a circle varies directly as the square of its diameter and 

is equal to - 1 — — X diameter squared or . 7854 X d 2 . For example, 

a wirel inch in diameter has an areaof 1 X 1 X .7854 = .7854 inches, 
while the area of a wire 2 inches in diameter equals 2 X 2 X .7854 = 
3.1416 inches. Thus the second wire has twice the diameter of the 
first wire, and not only twice but four times the area of the first wire. 
The areas of round wires vary directly as the squares of their diameters. 



108 



PRACTICAL ELECTRICITY. 



IV. The resistance of a conductor of given length and cross-sec- 
tion depends upon the material of which it is made. For 
example, the resistance of 1,000 feet of copper wire y 1 ^- inch 
diameter (No. 10 B. & S.) is about 1 ohm, while the resist- 
ance of a piece of iron wire of the same length and cross- 
section is about 6.3 ohms, and a similar piece of German 
silver 12.8 ohms. Law IV, Fig. 102. 





LAW 1— 




li 2 '' 


No. 10 B. & S. Copper Wife 


Resistance 1 Ohm 








No. 10 B. & S. Copper. Tubing 


Resistance JiOhms 



^LAW 1-- 



No. 10 B. & S. Copper Wire 
Resistance \ Ohm 



300 feet- 



1000 feet 



H2 



No. 10 B. & S. Copper Wire 



Resistance 1 Ohm 



1000 feet- 





LAW. 3 




i ms 


No. m B. & S. Copper Wire 


Resistance 4 Ohms 


I 




1000 feet J 



-IS 

_± — 



No. 10 B. & S. Copper Wire 



Resistance! Ohm 



1000 feet 





LAW 4 






No. 10 B. & S. Copper Wire 


Resistance 1 Ohm 


l< 1000 feet J 



No. 10 B. & S. Iron Wire 



Resistance 6.3 Ohms 



-B 



1000 feet 





LAW 5 


iH 2 


No. ,0 B. 8, S. Coppe, Wi re Jmfmlm ^fZlXT 


r 


— - 1000 feet J 



No. 10 B. & S. Copper Wire 



Resistance 1.0525 Ohms 



Temperature 100° Fahrenheit 



H£ 



1000 feet- 



No. 10 B. _& S. Copper Wire 



Resistance .9475 Ohms- 



Temperature 50° Fahrenheit 



1000 feet 



Fig. 102. — Laws of Resistance for Electrical Conductors. 



. RESISTANCE. 109 

V. The resistance of a conductor depends upon the temperature 
and is affected by any other cause ivhich modifies its molecular 
condition. The comparative resistances of the copper, Ger- 
man silver, etc., in Law IV, are only true for a definite tem- 
perature. If these substances are heated the resistance of 
the copper is increased nearly 10 times as much as that of 
the German silver, and 20 times as much as an alloy called 
platinoid. Law V, Fig. 102. 

All metals have their resistance increased by an increase of 
temperature. Carbon and all electrolytic conductors {battery solu- 
tions) decrease in resistance as the temperature increases. The 
resistance of copper increases about one-quarter of one per 
cent (.0021) for each degree temperature rise, Fahrenheit scale. 
See ^[ 262. The hot resistance of the carbonized filament of 
an incandescent lamp is about one-half the cold resistance. 

VI. The resistance of a conductor is always constant at the same 
temperature, irrespective of the strength of current flowing through 
it, or the electromotive force of the current. If a conductor offers 
5 ohms to a current of one ampere, it offers the same amount 
to a current of 10 amperes (provided the temperature is 
constant). 

128. Calculation of Resistance. — One foot of copper wire 
•nnnr inch diameter has a resistance of 10. 79 ohms at 75° 
Fahrenheit. Ten feet will have 107.9 ohms. One foot of 
copper wire yinnr mcn diameter will have one-fourth the re- 
sistance, (-r 2 or-^ 2 ) or 10.79 divided by 4 = 2.69 ohms. If 

this last wire were iron it would have 6. 3 times the resistance, 
or 16.947 ohms. Resistance varies directly as the length, inversely 
as the cross-sectional area, and with the material of the conductor. 

Let R represent resistance in ohms ; 
L i ' length in feet ; 

D ' i diameter (expressed in thousandths of an inch ) ; 

K " resistance of 1 foot .001 inch diameter. 

Then by above statement : 

Resistance = K X Length 

d (squared) 

t? K XL 
or R= , 2 (16), 



110 PRACTICAL ELECTRICITY. 

Prob. 14: Find the resistance of 1000 feet of copper wire .1 inch 
in diameter. 

By Formula (16) E = ^-^- 

K for copper = 10. 79. 

.1 inch = 100 thousandths = 100 mils. 
Substituting, 

R = 10 - ?9x ra =1 - 079ohms - 

The value of K is constant for the same wire, but different 
for each metal, and for copper at 75° Fahr. it is 10.79 
ohms (K). The value of K for other metals can be taken 
from the table below, and the resistance of any wire can be 
calculated when its dimensions are known. The resistance ob- 
tained corresponds with the temperature for which K is given. 
The following table gives the resistance of a foot of wire, . 001 
inch diameter, or the values of K for different metals when 
the temperature is 68° Fahr. See % 262. K therefore is the 
resistance of 1 mil-foot. 

Table VI. —Resistances of a Mil-Foot of the Metals (Values of K). 
Silver, 9.84 Zinc, 36.69 German Silver, 128.29 

*Copper, 10.79 Platinum, 59.02 {Platinoid, 188.93 

t Aluminum, 17.21 Iron, 63.35 Mercury, 586.24 

Prob. 15 : Substitute an iron wire for the copper wire in Prob. 14, 
and find its resistance. 

By Formula (16) R = K * L . 
Substituting, 

E = 63 - 35x iTOro= 6 - 335ohms - 

K for iron = 63.35. 
Iron has thus about six times the resistance of copper. 

129. Wire Measure. — The Circular Mil. — In wire meas- 
ure a mil is one one-thousandth of an inch (j-qqq, or .001- 
inch, or 1 mil). The area of a round wire 1 mil in diameter 
is 1 circular mil. If the wire is 2 mils in diameter (yoVg-, or 
.002-inch, or 2 mils), then it has a circular mil area of 4 
circular mils, the result being obtained by expressing the di- 
ameter of the wire in mils and squaring it (multiplying it by 
itself). The circular mil is used as the unit of area in the 
calculation of round wires for electrical purposes (the square 
mil for rectangular wires). It is the area of a circle having 

* Copper is given at 75° Fahr., this being the average temperature under which it is 
used, 
t Value for annealed aluminum (conductivity 54). 
X German silver 49 parts, tungsten 1 part. 



A 
G> 

r 

| 

ait— . 




^7 MIL 
EQUALS 
.001 INCH 


Fig. 


103. — Area of the Large Circle 
Equals 9 Circular Mils. 



RESISTANCE. Ill 

a diameter of T7 Vtt mc ^ > hence the square of any diameter, 
expressed in thousandths of an inch, will give as a product 
the number of circular units that can be placed side by side 
in a square, the sides of which 
are equal to the diameter that 
has been squared, the united 
area of the small circles con- 
tained within such a square 
being equal to the area of the 
large circle. This is illustrated 
in Fig. 103, where the large 
circle represents a wire three 
mils in diameter, and the small 
circles are the circular mils (9) whose united areas equal the 
area of the large circle. One circular mil equals .000000785 
square inch. 

1. To FIND THE CIRCULAR MIL AREA OF ANY ROUND WIRE 

WHEN ITS DIAMETER IN INCHES IS KNOWN : 

Express the diameter as a whole number in mils and square it. 
Let d == diameter ; 

d 2 = diameter squared ; 
C. M. ±= circular mil area. 
Then, 

C. M. = d 2 (17). 

Prob. 16 : What is the circular mil area of a wire \ inch diameter? 

1 inch = ^ ; therefore, \ inch = ^ Q or 250 mils. 
By Formula (17) C. M. = d 2 = d X d = 250 X 250 = 62500 C. M. 

2. — To FIND THE DIAMETER OF ANY WIRE WHEN THE 
CIRCULAR MIL AREA IS KNOWN : 

Extract the square root of the circular mil area. The result is 
the diameter expressed in mils, 

ord=j/OTS (18). 

Prob. 17 : What is the diameter of a wire if the area is 6530 C. M. 
(No. 12 B. AS.)? 

By Formula (18) d = i/CTM. = ^6530 = 81 mils nearly, or .081 
inch diam, 

130. The Square Mil. — Circular mil area applies to 
round wires, and is nearly one-quarter (.2146) larger than 
the true square inch area of round wires. Many conductors 



112 PRACTICAL ELECTRICITY. 

now used are rectangular in cross-sectional area, so that it is 
sometimes necessary to find their equivalent area in round 
wire measure. One square mil equals .000001 square inch. 

3. To FIND THE AREA OF A RECTANGULAR WIRE IN SQUARE 

MILS : 

Express the dimensions in mils and find, the product of the di- 
mensions. The result is square mils. 

Let c = thickness (in mils) ; 
d = width (in mils). 
Sq. mils = cXd (19). 

Prob. 18 : A copper ribbon for a field coil measures f inch X i 
inch. Find its square mil area. 

| = .625, or 625 mils i = .125, or 125 mils. 
By Formula (19) Sq. mils = c X d = 125 X 625 = 78125 sq. mils. 

4. To CONVERT CIRCULAR MIL AREA INTO SQUARE MIL AREA : 

Multiply the circular mil area by .7854-. The result is square 
mils. 

One circular mil = .7854 square mil. 
Therefore 

sq. mils = C. M. X .7854 . . . (20) . 

Prob. 19 : What is the square mil area of a wire I inch diameter ? 
By Prob. 16 its C. M. area was calculated to be 62500 C. M. 
By Formula (20) Sq. mil area = C. M. X .7854 = 62500 X .7854 = 
49087.5 sq. mils. 

5. To CONVERT SQUARE MIL INTO CIRCULAR MIL AREA : 

Multiply the square mil area by 1.2732. The result is circular 
mils. 

One square mil = 1.2732 mils. 
Therefore 

C. M. =sq. mils X 1.2732 . . (21). 
Prob. 20 : Find the circular mil area of the copper wire in Prob. 18. 
By Prob. 18 Sq. mil area = 78125. 

By Formula (21) C. M. = sq. mils X 1.2732 = 78125 X 1.2732 = 
99468.75 C. M. 

131. The Wire Gauge. — A number of wire gauges have 
been originated by different manufacturers of wire, such as 
the B. & S. gauge (Brown & Sharpe Manufacturing Co.), 
commonly called the American gauge, which is the one gen- 
erally used in this country ; B. W. G. gauge (Birmingham 
Wire Gauge), known as the English Standard Gauge ; W. & M. 
gauge (Washburn & Moen Manufacturing Co.), etc. Tables 



RESISTANCE. 



113 



Table VII.— Copper Wire Table. 
American Wire Gauge (Brown & Sharpe). 

Giving weights, length and resistances of soft copper wires of Mathiessen's standard 
conductivity at a temperature of 24°C. (75.2 F). 



Gauge. 


Diameter 


Area. 


WEIGHT 


LENGTH. 


RESISTANCE. , 


A.W. G 

"B.4S. 


Iocbes- 


Circular Mils. 


Lbe. per 1000 ft. 


Lbs per ohm. 


Feet per lb. 


Feel per obm. 


Obma 
per I00U feel 


Ohms per lb 


0000 

000 

00 




0.4600 
4096 
0.3648 
0.3249 


211600 
167800. 
133100. 
105500. 


640.5 

508.0 
402.8 
319.5 


12890 
8107 
5101 

3207 


1.561 
1.969 
2.482 
3.130 


20130. 
15960. 
12660 
10040 


04967 
06264 
0.07898 
09960 


00007755 
0.0001234 
0.0001960 
0003118 


1 

2 
3 

4 


0.2893 
0.2578 
0.2294 
0.2043 


83690. 
66370. 
52630. 
41740. 


253.3 

200 .-9 
159.3 
126.4 


2017 
1269 • 
. 798.3 
501.8 


3 947 
4.977 
6 2^6 
7.914 


7963 
6314 
5008. 
3971 


1256 
1584 
1997 
2518 


0004957 
0.0007883 
0.001254 
001993 


5 

6 
7 

8 ' 


0.1819 
1620 
1443 
1285 


83100. 
26250. 
20820. 
16510. 


100.2 
.'79.46 
63.02 
49 98 


315.5 

198 5 
124.8 
78.49 


9.980 
(2.58 
15.87 
20.01 


3149 

2497 
1981 
1571 


3176 
0.4004 
5048 
6367 


003170 
0.005039 
0.008012 
01274 


9 
10 
11 
1? 


0.1144 
0.1019 
0.09074 
0.08081 


13090. 
10380. 

8234. 

6530 


39.63 
31 43 
24 93 
19.77 


49.37 
31 04 
19.52 
12 28 


25.23 
31.82 
40.12 
50.59 


1246. 

987.8 
783.6 
621.2. 


8028 

1 012 
1 276 
1 610 


0.02025 
0.03221 
05122 
0.08144 


13 
14 
15 

16 


07196 
0.06408 
0.05707 
0.05082 


5178. 

4107. 
3257 
2583. 


15.68 
12.43 

9.858 
7.818 


7.'722 

4.857 
3 054 
1.922 


63.79 
80.44 
101.4 
127.9 


492.7 

-390.7 

309.8 

, 245 7 


2.029 
2 559 
3.227 
4 070 


0.1295 
0.2059 
0.3274 
5206 


17 

18 - 

19 

20 


04526 
0.04030 
0.0358'J 
0.03196 


2043 
1624. 
1288. 
1022. 


6.200 
4.917 
3.8S9 
8.092 


1.206 
0.7599 
0.4779 
0.3005 


161. 3 

203.4. 
256.5 
323.4 


194.9 
154 5 
122.5 
97.14 


5 132 
6.471 

8.160 
10.29 


0.8277 
1.316 
2.092 
3.328 


21 
22 
23 
24 


0.02846 
0.02535 
0.02257 
0.02010 


810.1 

642.4 
509.5 
404.0 


2.452 
1.945 
1.542 
1.223 


0.1890 
0.1189 
0.07475 
0.04702 


407.8 
514.2 
648.4 
817.6' 


77.07 
61.10 
48.47 
38.43 


12*97 
16.37 
20.63 
26.02 


5 291 
8.413 
13.38 
21.27 


25 
26 
27 

28 


0.01790 
0.01594 
0.01420 
0.01264 


320.4 
254.1 
201 5 
159.8 


0.9699 
0.7692 
0.6100 
0.4837 


0.02956 
0.01859 
0.01169 
0.007359 


1031 
1300 
1639. 
2067 


30.49 
24.17 
19.17 
15.20 


32.80 
41.37 
52.16 
65.78 


33 83 
53.78 
85.51 
135.9 


29 
30 
81 
82 


0.01126 
0.01003 
0.008928 
0.007950 


126.7 
100.5 
79.70 
63.21 


0.3836 
0.3042 
0.2413 
0.1913 


0.004626 
0.002909 
0.001829 
0.001150 


2607. 
3287. 
4145. 
5227. 


12.06 
9.563 
7.583 
6.013 


82.94 
104.6 
131.9 
166.3 


216.2 

343 8 
546.6 
869.2 


83 
84 
35 
86 


0.007080 
0.006305 
0.005615 
0.005000 


50.13 
39.75 
81.5a 
25.00 . 


0.1517 
0.1203 
0.09543 
0.07568 


0.0007237 
0.0004550 
0.0002863 
0.0001800 


6591. 

8311. 
10480. 
13210. 


4.768 
3.781 
2.999 
2.378 


209.7 
264.5 
333.4 
420.5 


1382. 
2198. 
3493. 
5556. 


37 
88 
89 
40 


0.004453 

0.003965 
0.003531 
0.003145 


19.83 
15.72 

12.47 
9.888 


0.06001 

0.04759 

0.03774 

. 0.02993 


0.0001132 
0. 00007101 
0.00004478 
0.01)002816 


16660. 
21010. 
26500. 
33410. 


1.886 
1.496 
1.186 
0.9408 


530.2 
668.5 
843.0 
1063. 


8834. 
14080. 
22330. 
35510. 



This table is based on the following values : - Resistance in terms of the international 
ohm. Specific gravity of copper = 8.89. Mathiessen's standard resistivity, one metre- 
gramme of soft copper = 0.14365 B. A. U. at 0°C, 0.141729 international ohms at 0°G. 
Mathiessen's temperature coeflicient = 1.09612 at 24°C. 



of these gauges will be found in the Appendix. The above 
(Table VII) gives the B. & S. gauge. The first column 
gives the manufacturer's number ; for example, the scale in 
B. & S- gauge is from No. 0000 (four naughts) wire (460 
mils diam., nearly \ inch) to No. 40 (3 mils diam., or yfVo 



114 PRACTICAL ELECTRICITY. 

inch), the sizes decreasing as the gauge numbers increase. 
The diameter, C. M. area, weight, length and resistance are also 
given for each size of wire. 

132. Wire Calculations. — Case 1. — Given Length and 
Area of Any Wire to Find Its Resistance : 

The resistance of any wire is equal to its length multiplied by the 
resistance of a mil-foot (K) and this product divided by its area. 
Let L = length of the wire (in feet) ; 
R = resistance (in ohms) ; 
C. M. == circular mil area (diam 2 ) ; 
K = resistance of one mil-foot. 
Then, 

R =lr • • • • < 22 >- 

Prob. 21 : A copper wire has a cross-sectional area of 8234 C. M. and 
is 1050 feet long. What is its resistance ? 

By Formula (22) R = ^ ^ L . K for copper = 10.79. 

j, 10.79X1050 , on , 
= 82S4 == ohms. 

L= 1050 feet. C. M. =8234. 

Case 2. — Given Resistance and Area to Find the 
Length : 

The length of any wire is equal to its resistance, multiplied by 
its circular mil area, and this product, divided by the resistance 
of a mil-foot (K). 

T R X C. M. 



K 



(23). 



Prob. 22 : What is the length of German silver wire wound on a 

resistance spool, if its resistance is 500 ohms and the size of wire No. 

20 B. & S. ? 

„ „ . /OON _ EX CM. 500X1022 onco _, , 
By Formula (23) L = = = — - — = 3983.16 feet. 

R = 500 ohms, C. M. = 1022, K .= 128.29. 
No. 20 B. & S. = 1022 mils (from Table VII). K for German silver 
= 128.29 (from Table V). 

Case 3. — Given Length and Resistance to Find the 
Area : 

The area in circular mils of any wire is equal to its length 
multiplied by the resistance of a mil-foot (K) and this product 
divided by its resistance. 



RESISTANCE. 115 

C.M.^^-? (24). 

Prob. 23 : What is the circular mil area of 1,000 feet of a certain 
iron wire, if its resistance is 30 ohms? 

By Formula (24) C. M. = ^ = 10"" X 63.35 _ 2m g & M 

K for iron = 63.35 from Table V. 

L — 1000 feet, R = 30 ohms, K = 63.35. 

Case 4.— Given the Area to Find the Weight. 

The weight per mile (5280 feet) of any bare copper wire is 
equal to the area in circular mils divided by the constant 62.5. 
Copper wire weighs about 555 pounds per cubic foot ; iron 
wire weighs about 480 pounds per cubic foot. 

C M 
Pounds per mile (bare copper wire) = ' J . . . (25). 

Pounds per foot (bare copper wire) = fi -^- _ * * (26). 

C. M. 
Pounds per mile (bare iron wire) e= „ ~ . . . (27). 

Prob. 24 : The circular mil area of a No. 10 B. & S. wire is 10,380. 
How many pounds of bare copper wire will be required for two lines 
running a distance of 5 miles? 

By Formula (25) lbs. per mile = ' ' = '*_ - = 166.08 lbs. per mile. 
1 \ j f 62>5 62 .5 r 

166.08 X 5 X 2 1660.8 lbs. 

133. Table of Conductivity and Resistivity of Metals. 

Silver being the best conductor has consequently the 
highest conductivity. In the following table the first column 
gives the conductivities, and the second the resistivities. The 
conducting power of silver being noted as 100, the values for 
all other metals are proportionally less. On the other hand, 
if the resistivity of silver be taken as 1, all the other metals 
will have proportionally higher values. 
Table VIII.— Comparative Conductivity and Resistance of Metals. 

Conductivity. Resistivity. 

(Comparative (Comparative 

Conductance.) Resistance.) 

Silver (annealed) 100. 1. 

Copper (annealed) 99. 1.01 

Silver-copper alloy (equal parts) 86.6 1.15 

Gold (annealed) 78. 1.28 

Aluminum 54. 1.84 

Zinc 30. 3.3 

( Continued on following page. ) 



116 



PRACTICAL ELECTRICITY. 



{Table VIII concluded. 



Conductivity.. 
(Comparative 
Conductance.) 



Eesistivity. 

(Comparative 

Resistance. ) 

6.21 

6.25 

9.43 
11.2 
12.6 
13.3 
19.2 
25.6 
62.5 
83.3 



Brass (according to composition) . . . 

Iron 16.1 

Tin 15.5 

Platinum 10.6 

Lead 8.9 

Nickel 7.9 

German silver 7.5 

Platinoid (Ger. silver 49 parts, tungsten 1) . 5.2 

Antimony 3.9 

Mercury 1.6 

Bismuth 1.2 

RELATIVE RESISTANCES. 

Nitric acid— commercial value— @ 15 to 28°C 1,100,000 

Sulphuric acid— 1 to 12 parts water—® 15 to 28°C 2,000,000 

Common salt— saturated solution—® 15 to 28°C 3,200,000 

Sulphate of copper 18,000,000 

Distilled water— not less than 10,000,000,000 

Glass—® 200°C 15,000,000,000,000 

Gutta percha— @0°C 5,000,000,000,000,000,000,000 

134. Internal Resistance of a Bat- 
tery. — Resistance in a voltaic circuit 
may be divided into two parts ; inter- 
nal resistance (r), which the current 
encounters in passing through the 
liquid from one plate to the other, and 
external resistance (R), or that of the 
outer circuit. See Fig. 104. The 
current that a cell will give, therefore, 
depends upon its internal resistance, 
and will be greater the less this resist- 
ance, and vice versa. The internal re- 
sistance is governed by the same laws 
as the external resistance. Thus : 




Fig. 104.— The Internal 
and External Resist- 
ance of a Cell. 



r (internal resistance) = 



KX 



distance of plates apart (L) 



areas of plates submerged (d 2 ) 
or the internal resistance varies with 

(1) The electrolyte used, 

(2) Distance of plates apart, 

(3) Size, or area of plates. 

A good battery, therefore, should have a low internal re- 
sistance. 



RESISTANCE. 117 

QUESTIONS. 

1. The conductivity of a porcelain rod is very low. How will this 
affect its insulating qualities ? 

2. What is the function of an insulator ? 

3. The resistance of 5 pounds of No. 36 platinoid wire is very high. 
How does this affect the conductivity ? 

4. A battery sends 5 amperes through a piece of copper wire. Would 
the same cell send more or less current through another piece of cop- 
per wire twice as long but of double the area of the first piece ? 

5. If the second wire in question 4 was twice the length and twice 
the diameter of the first wire, what would be your answer ? 

6. Current from a cell flowing through a piece of iron wire deflects 
a galvanometer needle 40 degrees. When a piece of aluminum of 
similar dimensions to that of the iron is substituted, the deflection is 
55 degrees. How do you account for this, since both wires are exactly 
the same size ? 

7. The resistance of an incandescent lamp is 500 ohms cold. Will 
it be more or less when the lamp is lighted? Why? 

8. One mile of a certain iron wire has a resistance of 6 ohms. What 
will be the resistance of one-quarter of a mile of the same wire ? 

PROBLEMS. 

1. The insulation of a wire measures 16.75 megs. What is its equiv- 
alent resistance in ohms ? Ans. 16,750,000 ohms. 

2. What is the circular mil area of a wire T 3 e inch in diameter? 
Ans. 35156 C. M. 

3. The circular mil. area of a wire is 5625. What is its diameter ? 
Ans. 75 mils. 

4. An armature is wound with copper bars T 3 g by f of an inch. 
What is their equivalent area in circular mils? Ans. 89522 C. M. 

5. The resistance of the series coil of a dynamo is .0065 ohm. 
Express its resistance in microhms. Ans. 6500 microhms. 

6. What is the square mil area of a No. 12 B. & S. copper wire ? 
Ans. 5128.662 sq. mils. 

7. What is the resistance of 5 pounds of No. 18 B. & S. wire, 
allowing 5 percent for insulation? Ans. 6.251 ohms. 

8. The coils of a rheostat, constructed of No. 8 iron wire, have a 
resistance of 10 ohms. What length of wire was required? Ans. 
2606.14 feet, 

9. A rectangular wire has a square mil area of 20616.75. What is 
the equivalent circular mil area ? Ans. 26249 C. M. 

10. What size of B. & S. wire has an equivalent area to the wire in 
Prob. 9 ? .4ns. No. 6. 

11. Calculate the resistance of 2000 feet of No. 6 B. & S. copper 
wire. Ans. 0.822 ohms. 

12. Construct from your own calculations by the use of formulae 
a wire gauge table for No. 12 B. & S. copper wire. Give circular mil 
area, square mil area, pounds per mile, pounds per foot, pounds per 
ohm, feet per pound, feet per ohm, ohms per pound and ohms per 
foot. 



LESSON XIII. 

OHM'S LAW AND BATTERY CONNECTIONS. 

Electromotive Force (Pressure) — Table IX. Electromotive Forces of 
Batteries and Dynamos — Ohm's Law — Ohm's Law Applied to a 
Battery Circuit —Methods of Varying Current Strength — The Size 
of a Cell — Cells Connected in Series to Increase the E. M. F. — 
Cells connected in Parallel or Multiple for Quantity — The Internal 
Resistance of Cells in Series — Current from Cells in Series — The 
Internal Resistance of Cells in Parallel or Multiple — Current from 
Cells in Parallel or Multiple— Advantage of Parallel Connection — 
Advantage of Series Connection — Cells Grouped in Multiple 
Series— Internal Resistance of Any Combination of Cells — 
Current Strength from Any Combination of Cells— Cells Con- 
nected in Opposition— Questions and Problems. 

135. Electromotive Force (Pressure). 

Exp. 41 : Connect a Daniell cell in series with spool 4 of resist- 
ance spool set, fl 124, and a detector galvanometer, and note the value 
of the deflection; Now substitute a bichromate cell for the Daniell 
cell, using the same spool, and the deflection is greater than before. 
The E. M. F. of the bichromate cell is higher than that of the Daniell 
cell, and therefore causes a larger current to flow 7 through the same 
resistance. Any other type of cell used would cause more or less cur- 
rent to flow through the spool, depending upon its E. M. F. (pressure 
in volts). 

In a battery, the E. M. F., which is the primary cause of 
the current, is dependent on the nature of the plates and the 
solution used, but independent of their size or distance apart. 

In a dynamo the E. M. F. is set up by revolving a bundle 
of wires in a magnetic field, and depends upon the strength 
of the field, the number of wires revolved, and the speed. 

136. Electromotive Force of Batteries and Dynamos. — 
The following table gives the electromotive forces of the 
different cells described in Lesson IX : 

Table IX— E. M. F. of Batteries. 

Bunsen 1.75 to 1.95 volts. Grove 1.75 to 1.95 volts 

Chloride of Silver , 1.1 " Harrison ... 2.5 

Daniell 98 to 1.08 " Leclanche type 1.4 to 1.6 

Dry cell .... 1.4 " Partz 1.95 to 2. 

Edison-Lalande .7 " Smee .65 

Grenet type . .1.8 to 2.3 " Storage battery 2.1 

Dynamos generate from a few volts to thousands of volts, according 
to the purpose for which they are designed. 
118 



OHM'S LAW AND BATTERY CONNECTIONS. 119 

Incandescent lighting dynamos, direct current 125 volts 

Alternating current dynamos, at brushes 1000 to 2000 volts 

Electric railway generators (direct current) 550 volts 

Electroplating dynamos 2 to 6 volts 

Magneto generators . . 700 to 2000 volts 

Commercial power circuit generators 250 to 500 volts 

Series arc light dynamos 2800 to 8000 volts 

137. Ohm's Law. — In any circuit through which a 

CURRENT IS FLOWING WE HAVE THE THREE FOLLOWING FAC- 
TORS present : ( 1 ) The pressure or potential differ- 
ence, EXPRESSED IN VOltS, CAUSING THE CURRENT TO FLOW. 

(2) The opposition or resistance of the circuit, ex- 
pressed in ohms, WHICH MUST be overcome before the 
current can flow. (3) The current strength, expressed 
in amperes, which is maintained in the circuit, as a 
result of the pressure overcoming the resistance. A 
definite and exact relation exists between these three 
factors, pressure, current strength, and resistance in 
any circuit, whereby the value of any one factor may 
always be calculated when the values of the other two 

FACTORS ARE KNOWN. THIS RELATION, KNOWN AS Ohm's Law, 

is very important*, since it forms the basis for all 

CALCULATIONS IN ELECTRICAL ENGINEERING. It MAY BE SUM- 
MARIZED AS FOLLOWS : 

First. — The current strength in any circuit is equal to 
the electromotive force applied to the circuit, divided 
by the resistance of the circuit.f 

Let E = E. M. F., potential difference or available pressure, 
expressed in volts, applied to any circuit ; 
R = Resistance of the circuit, expressed in ohms; 
= Current strength, expressed in amperes, to be main- 
tained through the circuit J. Then by the above 
statement 

- . Pressure 

Current = 35^55^ 

. Volts 

or Amperes = 0^. 

or C=z| (28). 

* Lesson XX is devoted to a further discussion of the practical application of 
Ohm's Law. 

t Ohm's Law, as stated above, applies to direct currents flowing in any circuit. It 
is modified to some extent in alternating current calculations. See fl 297. 

X I is used in some books as the symbol for current strength. 



120 PRACTICAL ELECTRICITY. 

The following five statements and formulae are directly 
derived from the above general statement of Ohm's Law, and 
are all therefore included in the expression C = E ~ R. 

Problems are solved under each case to illustrate the inter- 
pretation of each statement made.* 

Prob. 25 : An incandescent lamp has a resistance (hot) of 220 ohms, 
and is connected to an electric light main, across which 110 volts 
potential difference is maintained. What current will flow through 
the lamp? 

By -Formula (28) C = j> = ooq ~ o am P ere * 

E ==■ 110 volts, R =-220 ohms. 

Second. — The current strength in any circuit increases or de- 
creases directly as the E. M. F. , or potential difference, increases 
or decreases* when the resistance is constant. With a constant 
pressure the current increases as the resistance is decreased, and 
decreases as the resistance is increased, or briefly, the current 
varies directly as the E. M. F. and inversely as the resistance. 

C = =d, with R constant, C varies directly as E. With E 

constant the greater R, the less C, and vice versa. 

Prob. 26 : In Prob. 25, if the pressure is increased to 440 volts, what 
current will the lamp receive ? 

By Formula (28) C = =™ = 99a = 2 amperes. 

E =- 440 volts, R = 220 ohms. 

This problem illustrates the increase of C with increase of E with a 
constant R. 

Prob. 27 : In Prob. 25, if the pressure is reduced to 55 volts, what 
current will the lamp receive ? 

By Formula (28) C = =5 = oon = 4 am P ere * 

E = 55 volts, R = 220 ohms. 

This problem illustrates the decrease of C with the decrease of E 
when R is constant. 

Prob. 28 : In Prob. 25 the voltage is again 110, but a lamp of HO 
ohms resistance is used. What current will it receive? 

By Formula (28) C f= ~ = ^ = 1 ampere, 
xv 110 

E = 110 volts, R = 110 ohms. 
With E constant, C increases as R decreases. 

* Some problems refer to cells and circuits connected thereto, but the principles 
and connections are the same as those involved in direct current, electric lighting, 
and power calculations. Problems on these subjects are given in later lessons. 



OHM'S LAW AND BATTERY CONNECTIONS. 121 

Prob. 29 : In Prob. 25 the pressure is 110 volts and another lamp 
of 440 ohms is used. What current will it receive ? 

By Formula (28) C = |=^ = ^ ampere. 

E = 110 volts, E =440 ohms. 
Therefore, as R increases, when E is constant, C decreases. 

Third. — The electromotive force required to maintain a certain 
current strength in a circuit of known resistance, is numerically 
equal to the product of the current strength and the resistance. 
E = C x.R- 

By the above statement, 

Pressure = Current Strength X Resistance, 
or Volts = Amperes X Ohms, 

or E = C XR (29). 

Prob. 30 : What pressure is required to cause 10 amperes to flow 
through an arc lamp if the resistance (hot) is 4.5 ohms ? 

By Formula (29) E = C X R= 10 X 4.5=45 volts. 
C = 10 amperes, R = 4.5 ohms. 

Fourth. — The pressure varies directly as the current and re- 
sistance. For example, if a greater current is to be sent through 
the same resistance, a greater pressure must be applied ; also, if the 
same current is to be passed through a higher resistance a greater 
pressure must be applied. E = C X R. 

Prob. 31 : What pressure is required to cause 15 amperes to flow 
through the lamp in Prob. 30? 

By Formula (29) E = C X R= 15 X 4.5 = 67.5 volts. 
C = 15 amperes, R = 4.5 -ohms. 

Prob. 32 : If the lamp in Prob. 30 had a resistance of 9 ohms, what 
pressure must have been applied to have 10 amperes flow through it ? 

By Formula (29) E = CxR = 10X 9 = 90 volts. 
= 10 amperes, R = 9ohms. 

Problems 31 and 32 illustrate how E increases directly with R and 
C. If either R or C had been decreased E would have been decreased 
also. 

Fifth. — The resistance required to be inserted in any circuit, so 
that a given current will flow by reason of a known pressure, is 
equal to the pressure to be applied, divided by the current strength 

that is to be maintained. R = —• 



122 PRACTICAL ELECTRICITY. 

Bv the above statement, 

Resistance = ~ Press ure 

Current strength 

or Ohms VoltS 



Amperes 

or R = fj (30). 

Prob. 33 : An electric heater is constructed of No. 18 iron wire and 
sufficient heat is radiated when the wire carries 10 amperes. The 
heater is placed across 110 volts. What will be the value of its hot re- 
sistance ? 

By Formula (30) R = ~j = ^° = 11 ohms (hot). 
E = 110 volts, C = 10 amperes. 

Sixth. — Tlie resistance required for any circuit varies directly 
with the pressure applied, and inversely as the value of the current 
to be maintained. For example, with a constant pressure the 
resistance must be halved if the current is to be doubled ; on 
the other hand, with a constant current to be maintained in a 
circuit at double the pressure, the resistance must be doubled. 

Prob. 34: In Prob. 33 the current required is 20 amperes and the 
pressure the same as there given. What will be the hot resistance 
required ? 

By Formula (30) R = t^= -^-=5.5 ohms. 

E = 110 volts, C = 20 amperes. 

Prob. 35 : If the pressure is 220 volts in Prob. 33, what resistance 
will be required? 

By' Formula ( 30 ) R = ? = 22C) = 22 ohms. 

E = 220 volts, C = 10 amperes. 
Problems 34 and 35 illustrate the sixth statement made above. 

138. Ohm's Law Applied to a Battery Circuit. — When 
the total E. M. F. is used in Ohm's Law, the total resistance of 
the circuit must also be used in calculating the current strength. 
For example, when an electromagnet of .4 ohm is connected 
to a cell of 2 volts E. M. F. the current through the spool 
will not be E -*- R or 2 -*- .4 — 5 amperes, as might first be 
supposed. It requires a certain portion of the 2 volts to cause 
the current to flow through the cell's internal resistance. 
The internal resistance must be added to the external resistance to 
obtain the total resistance of the circuit, which is to be divided into 
the total pressure to obtain the current strength. If the internal 



OHM'S LAW AND BATTERY CONNECTIONS. 123 

resistance of the above cell is .6 ohm, then the total resistance 
is .4 -f- .6 = 1 ohm, and the current equals E -s- R = 2 -*- 
i = 2 amperes, or less than one-half of our first result. 

Let R= the total external resistance of the circuit (in ohms) ; 
r = the internal resistance of the circuit (in ohms). 
Then R-|-r = total resistance of the circuit (external -j- 
internal) . 

Then Ohm's Law becomes, 

° = R^ < 31) - 

Small r represents the internal resistance, in ohms, of a cell, 
or the resistance of the windings of a dynamo, which would 
be the dynamo's internal resistance. 

Prob. 36 : If a bichromate cell, E. M. F. 2 volts, internal resistance 
.5 ohm, is connected to an electromagnet having a resistance of 1.5 
ohms, what current will the magnet receive ? 

F 2 

By Formula (31 ) C = - p , = = = . = 1 ampere. 

E = 2 volts, R=1.5 ohms, r=.5 ohm. 
Ohm' s Law applies equally as well to any part of a circuit as 
to the whole circuit. When applied to part of a circuit, 
care must be exercised to use the value of the pressure applied 
to the resistance of that portion of the circuit considered, when 
E will still represent the volts applied and R the resistance of 
the part of the circuit to which E is applied. When E is 
used as the total pressure, R, to correspond, must be the 
total resistance. When E is used as the pressure applied to 
part of a circuit, R must be the resistance of that part to 
which this pressure is applied. This double application of 
the law is illustrated in Probs. 36, 37, 38, and 39, which 
should be carefully studied. 

Prob. 37 : The E. M. F. of a cell is 2 volts, its internal resistance, 
.5 ohm. A number of different resistance spools are joined together 
in series and connected to the cell. By electrical measurement it is 
found that the pressure causing the current to flow through a .4 ohm 
spool is .6 volt. What is the value of the current flowing through 
this spool ? Make a sketch of the circuit. 

E 6 
By Formula (28) C = p = '-7 = 1.5 amperes. 

E --= .6 volt, R = .4 ohm. 

Since the current is the same in all parts of a series circuit, 

1.5 amperes must flow through each of the other spools men- 



124 PRACTICAL ELECTRICITY. 

tioned ; also through the internal resistance of the cell. This 
problem also illustrates the difference between E. M. F. and 
potential difference. See ^| 70. The difference of potential, 
or pressure between the spool terminals, is .6 volt, while the 
E. M. F. is 2 volts. In Ohm's LawE represents either value. 
See 1[ 138, also Lesson XX. 

Prob. 38 : What portion of the total E. M. F. in Prob. 37 is used in 
overcoming the internal resistance of the cell? 

By Formula (29) E = C X R, 

from which is derived E =C X r (32). 

This gives the pressure lost or volts drop inside the cell, fl 230. 

By Formula (32) E = CXr = 1.5x.5=.75 volt. 
C — 1.5 amperes, r = .5 ohm. 

Prob. 39 : What portion of the E. M. F. is available for the other 
spools in the series circuit of Probs. 37 and 38 ? 

By Formula (30) R = ^ = ^ = 1.333 ohms (R + r) 

E = 2 volts, C =1.5 amperes. 
Resistance of cell (.5) plus resistance of one spool (.4) = .9 ohm. 

1.333 — .9 = .433 ohm for balance of spools. 
By Formula (29) E = C XR = 1.5 X .433 = .6495 volt. 

C = 1.5 amperes, R = .433 ohm. 

From Formula (31) C = x? i r we may also change Formulae (29) 
and (30) to include the internal resistance, as follows : 
By Formula (29) E = X R. 
Substituting E = CX(R + r) (33). 

By Formula (30) R=^; 

E 

substituting (R 4- r) = q ; 

E 
by transposition R = ^ — r (34). 

Also r = C~~ R t 35 )' 

Prob. 40 : A cell with an internal resistance of 2 ohms sends a cur- 
rent of .035 ampere through the electromagnets of a bell having a 
resistance of 48 ohms. What is the E. M. F. of this cell ? 

By Formula (33) E =C X (R + r) = .035 X (48 + 2) = .035 X 50 = 
1.75 volts. 

C = .035 ampere, R = 48 ohms, r = 2 ohms. 
Prob. 41 : A current of .25 ampere is maintained through a circuit 
by an E. M. F. of 2 volts ; the internal resistance of the cell is 1.5 
ohms. What is the value of the external resistance? 

By Formula (34) R=q — r = ^g — 1.5 = 6.5 ohms. 
E = 2 volts, C = .25 ampere, r = 1.5 ohms. 



OHM'S LAW AND BATTERY CONNECTIONS. 125 



139. Methods of Varying Current Strength. — By 

Ohm' s Law the current through any circuit may be regulated 
in two ways since C = E -*- R ; by increasing the pressure, E 
(the dividend), or by decreasing the resistance, R (the divi- 
sor), the current strength, C (the quotient) will be increased ; 
or by decreasing the pressure, or increasing the resistance the 
current will be decreased. For example, 25 volts will cause 
5 amperes to flow through 5 ohms. C = E^- R. If the 
pressure is raised to 35 volts the current strength will be 7 
amperes. Current from any cell may thus be decreased by 
inserting resistance in the cell circuit. If sufficient current, 
however, cannot be obtained from a cell, and as the E. M. F. 
is a fixed quantity for each type of cell, the E. M. F. may 
be increased by joining two or more cells together, so that 
the total E. M. F. is the sum of the E. M. F.'s of the sepa- 
rate cells. This will be better understood from the hydraulic 
analogies in % 141. 

140. The Size of a Cell. — It has been stated that the 
E. M. F. of a cell is the same for the same type of cell, without 
regard to size, but that the current depends on the size. In 
Fig. 105 the cylindrical tank, A, has a capacity of 100 gal- 
lons of water under a pressure of 10 pounds per square inch, 
due to the weight of the piston. Neglecting the weight of 
the water, the pressure gauge will record a pressure of 10 
pounds. When the valve is opened the water will be dis- 
charged at the 
rate of about 
one gallon per 
minute, under a 
pressure of 10 
pounds per 
square inch, so 
that at this rate 
it will require 
100 minutes to 
empty the tank. 

A similar tank, B, has a capacity of 10 gallons of water under 
a pressure of 10 pounds per square inch, due to the piston. 
Neglecting the weight of the water, the pressure gauge will 
record 10 pounds also. The diameter of the pipe is the same 
size as in tank A, and when this valve is opened the water will 
flow out at the rate of one gallon per minute under a pressure 



looS-o-flg^Uwfc 



\o5-cM>v^2^vJi 




Fig. 105. — Two Cylindrical Tanks of Different Capaci- 
ties, Containing Water Under Pressure. 



126 



PRACTICAL ELECTRICITY. 



of 10 pounds per square inch as before, thus requiring only 
ten minutes to empty tank B. In both tanks the pressure and 
the rate of flow are the same, but tank A will maintain the 

current of 



sv 



Cc£CA 



Zip 



€UU> 







etwv^^t^^XLVV^C^ig 



Fig 



'C& 



106.— Two Cells of Different Size but Having the 
Same E. M. F. 



water ten 
times as 
long as tank 
B. Now 
consider 
Fig. 106, in 
which the 
large cell A 
has a ca- 
pacity of 
100 am- 
pere-hours (see H 117) and an E. M. F. of 2 volts. When 
the switch is closed the galvanometer indicates, say 45 
deflections, corresponding to a current strength of one ampere, 
and sufficient chemicals and zinc are present to maintain this 
current for 100 hours when the pressure is 2 volts and the rate 
of flow one ampere. Consider now a similar small cell B, 
which has a capacity of 10 ampere-hours and an E. M. F. of 
2 volts. When the switch is closed through the same gal- 
vanometer the deflections are 45, as before, corresponding to 
a current strength of one ampere, sufficient chemicals and 
zinc being present to maintain this current for only 10 hours 
when the pressure is 2 volts and the rate of flow one ampere 
(neglecting the internal resistance). Thus the quantity of 
electricity depends on the size of the cell. If a large drain 
pipe had been used in tanks A and B, they would have been 
emptied more rapidly since the rate of flow would have been 
greater. If a galvanometer wound with a larger wire had 
been used, the cells A and B would not have maintained the 
current for so long a time, the rate of flow being greater. 

141. Cells Connected in Series to Increase the E. M. 
F. — Consider the hydraulic analogy in Fig. 107, where the two 
similar cylindrical tanks A and B have a capacity of 100 gal- 
lons each. The pressure on the water in tank A and con- 
necting pipe C is 10 pounds per square inch, due to the 
weight of the piston, so that the pressure gauge No. 1 indi- 
cates 10 pounds per square inch. In tank B the pressure on 
the water is 10 pounds per square inch, due to the pressure of 



OHM'S LAW AND BATTERY CONNECTIONS. 127 



±1 















the piston on tank A above it, plus 10 pounds per square inch, 
due to the weight of its own piston, so that gauge 2 will reg- 
ister 20 pounds per square inch. The weight of the water is 
neglected. When the valve in 
the drain pipe of tank B is 
opened this tank will deliver 
the same quantity of water 
(100 gallons) as would be 
delivered by tank A, but at 
double the pressure. The rate 
of flow is, therefore, twice as 
rapid. If a number of similar 
tanks were connected in like 
manner above A, the pressure 
on gauge 2 would be increased 
10 pounds per square inch for 
each tank added, although the 
quantity of water delivered 
through the valve would be the 
same as that of one tank. Con- 
sider now Fig. 108, where two 
cells, each having a capacity of 
100 ampere-hours, and an E. 
M. F. of 2 volts are joined 
together so that the E. M. F.'s are in the same direction. 
The carbon pole of the first cell is connected to the zinc pole 
of the second cell, and the two remaining + and — terminals 




'/vvwfr&f 



JAAAAbtt 6 

Fig. 107.— Two Cylindrical Tanks, 

Full of Water, Connected in 

Series for Pressure. 

Gauge 2 records twice the pressure indi- 
cated upon gauge 1. 



connected to the galvanometer. 



lOO tOwvp 



Cells connected in this manner 
are joined in series. The 
total pressure applied to 
the galvanometer when 
the switch is closed is twice 
the pressure of one cell 
(neglecting internal re- 
sistance) or 4 volts. The 
total quantity of electricity 
that will pass through the 
galvanometer is the same 
as would be delivered by 
each cell separately, 100 ampere-hours, although, since it 
is delivered at twice the pressure of a single cell, the rate 
pf flow is twice as great as with- on§ cell, When -a number 




Fig. 



108. — Two Cells Connected in Series 
for Pressure. 

The galvanometer indicates twice the pressure 
of one cell. 



128 



PRACTICAL ELECTRICITY. 



of similar cells are thus connected in series the pressure 
applied to the galvanometer will be increased by 2 volts for 
each cell so added, but the total quantity of electricity that 
can be delivered will be equal to the capacity of only one cell. 
142. Cells Connected in Parallel or Multiple for Quan- 
tity. — In Fig. 
109. two similar 
cylindrical tanks 
have a capacity 
of 100 gallons of 






rami 



MMM 



-^^■—?%J3X<A/- 



\o£Z« 

iiiiii ii i iirri iiii 



.%<aXestS— ■ 



tiaJUv 



I 



/J/MMutfJ. 



o«*f 



Fig. 109.— Two Cylindrical Tanks, Full of Water, 
Connected in Parallel for Quantity. 

The pressure gauge records the pressure due to only one tank, 

but the quantity of water delivered is equal to 

the sum of the two capacities. 



water each, and 
are connected by 
a pipe, C, in 
which a pressure 
gauge is attached. 
The piston in 
each tank exerts 
a pressure of 10 
pounds per 

square inch, but the pressure gauge records only 10 pounds 

pressure, the same as though only one tank were used. The 

addition of any number of similar tanks will not increase the 

pressure, which will always remain 10 pounds per square inch. 

The weight of water is 

neglected. Although the 22*j£~± 

pressure is not increased, }\ kl 

the quantity of water IB 

which can be drawn from 

the valve in the drain 

pipe increases in propor- 
tion to the number of 

tanks so added ; thus, the 

total capacity of 2 tanks 

is 200 gallons ; 6 tanks, 

600 gallons. ImFig. 107 

the tanks were arranged 

in series to add their 

pressures together, while 

in this case the tanks are 

arranged in parallel to add their volumes together. In a 

cell, the total quantity of electricity depends upon the 

amount of zinc to be acted upon. Suppose the cell gives 1 




110.— Two Cells Connected in Parallel 
for Quantity. 

The total capacity and E. M. F. of the two small 
cells are exactly equal to that of the larger cell. 



OHM'S LAW AND BATTERY CONNECTIONS. 129 

ampere-hour for each square inch of zinc exposed to the 
acid, then by increasing the area of the zinc plates a greater 
quantity of electricity can be obtained from the cell. This 
can be done in two ways : by making one very large cell, as 
B, Fig. 110, or by connecting the like plates of two or more 
smaller cells as in A, Fig. 110. Here the zinc plates of two 
cells are connected by a wire, forming one large zinc plate with 
double the area, the copper plates being similarly connected. 
Cells so connected are arranged in parallel or multiple. When the 
switch is closed in arrangement A the galvanometer is sub- 
jected to 2 volts pressure, neglecting internal resistance, 
which pressure would not be increased, no matter how many 
cells were thus connected. The total quantity of electricity 
that will flow through the galvanometer will increase in pro- 
portion to the number of cells so added. The two cells in A, 
therefore, could maintain 1 ampere through the galvanome- 
ter for 200 hours at a pressure of 2 volts, as could also the 
larger cell B. The advantage, then, of having small cells is 
that they can be arranged either for pressure or quantity, as 
may be desired, by connecting them in series or in multiple. 

Exp. 42 : Using a galvanometer of high resistance, compare the 
E. M. F.'s of different types of cells and record the deflections, the 
value of which will vary exactly as the E. M. F. varies. 

Exp. 43 : Connect unlike poles of two similar cells (which is 
termed joining cells in series) and attach the two remaining terminals 
to a high resistance galvanometer. The deflection is greater than 
with one cell, because - the E. M. F.'s of the cells have been added to- 
gether and greater pressure is applied to the galvanometer circuit. If 
the deflections are directly proportional to the current, their value 
will be nearly doubled. Add three similar cells in series and the 
pressure is three-fold, and so on. 

Exp. 44 : Connect two dissimilar cells in series (for example a 
Daniell cell, 1.1 volts, and Leclanche cell, 1. 5 volts) with a high re- 
sistance galvanometer, and the deflection is greater than with either 
cell alone. The pressure applied to the galvanometer is equal to the 
sum of the two pressures in series (1.1 -f 1.5 = 2.6 volts). 

Exp. 45: Record the deflections produced by one cell (say a 
Daniell) connected to a high resistance galvanometer. Using two 
similar cells, connect the positive poles by one wire, and the negative 
poles by another wire, and attach lead wires from these junctions to 
the galvanometer (when like poles are thus connected the cells are 
joined in parallel or multiple). The deflection is not perceptibly 
greater than with one cell, because the E. M. F. of two or more sim- 
ilar cells, joined in parallel, is the same as the E. M. F. of 1 cell ; 
hence, two Daniell cells in parallel, 1 volfc each, total E. M. F. 1 volt ; 
10 such cells in multiple, total E. M. F. 1 volt ; 10 such cells in 
series, total E. M f F. 10 volts. In the above experiments a galva- 
9 



130 PRACTICAL ELECTRICITY. 

nometer of many turns of fine wire is used, so that little current will 
flow from the cells, and the deflections represent nearly the true 
pressure, 1j 233. 

143. The Internal Resistance of Cells in Series. — 

When a number of cells are connected in series, and to an 
external circuit, the current flowing through the external cir- 
cuit must pass through each cell so connected, Fig. Ill, 
requiring, therefore, a certain fraction of the total E. M. F. to 
overcome the resistance of each cell. 

To. FIND THE TOTAL INTERNAL RESISTANCE OF A NUMBER 
OF SIMILAR CELLS CONNECTED IN SERIES : 

Multiply the resistance of one cell by the number so connected. 
Let r = internal resistance of 1 cell; 
ns = number (n) of cells in series (s). 
Then r X ns = total internal resistance of cells in series (36). 

I _, 





Fig. 111. — Eight Cells Connected in Series for Pressure. 
The pressure is eight times that of one cell, as is also the total internal resistance. 

Prob. 42 : Ten Daniell cells, with an internal resistance of 2 ohms 
each, are connected in series. What is the total internal resistance ? 
By Formula (36) total r = r X ns = 2 X 10 = 20 ohms, 
r = 2 ohms, ns = 10 cells. 

144. Current from Cells in Series. — To find the cur- 
rent THAT WILL BE MAINTAINED IN AN EXTERNAL CIRCUIT 
FROM A NUMBER OF CELLS IN SERIES : 

Find the total E. M. F. applied by multiplying the E. M. F. oj 
1 cell by the number connected in series. Find the total interned 
resistance by Formula {36). Then by Ohm's Lav) the Current 
equals the E. M. F. -*- the total resistance. 
Let E = E. M. F. of one cell ; 

r — internal resistance of one cell; 
ns = number of cells in series; 
R = external resistance. 

Then c=~ X ™. p (37). 

(r X ns) + R v J 



OHM'S LAW AND BATTERY CONNECTIONS. 131 

Prob. 43 : Ten Daniell cells are joined in series to two spools of 
wire in series, one 4 ohms, the other 6 ohms. E. M. F. of one cell — 
1 volt ; internal resistance of one cell = 2 ohms. What current will 
flow through the circuit ? 

v> v i /o~n r. EXns 1X10 10 1 

By formula (37) C= (r x n9) + r = (2 X 10) + 10 = 30 = 3 

ampere. 

E = 1 volt, ns = 10 cells, r = 2 ohms, R = 6 + 4 = 10 ohms. 

145. The Internal Resistance of Cells in Parallel or 
Multiple. — When a number of similar cells are connected in 
multiple, Fig. 112, and to an external circuit, the total cur- 
rent flowing through the external circuit does not pass through 
the resistance of each cell as in the series case, but is divided 
among the cells in proportion to the number in parallel. The 
internal path for the total current is of much lower resistance 




Fig. 112.— Eight Cells Connected in Parallel for Quantity. 

The pressure is the same as that of one cell; the total internal resistance one eighth of 

that of one cell; the current nearly eight times that of one cell. 

than the resistance of one cell. Cells connected in parallel 
have their like plates connected, Fig. 112, forming practically 
one large cell, the positive and negative plates of which are 
equal in area to the sum of the areas of the separate cells. 
The area of the conducting liquid is proportionately increased, 
and consequently, the internal resistance decreased. (See 

ir 134.) 

To FIND THE INTERNAL RESISTANCE OF A NUMBER OF CELLS 
IN PARALLEL : 

Divide the resistance of one cell by the number connected in 

'parallel. 

Let r = the internal resistance of one cell; 

nq = the number of cells in multiple or parallel. 

r 
Then — = total internal resistance of cells in parallel (38). 

Prob. 44 : In Prob. 43 the cells are joined in parallel. What is now 
the internal resistance ? 



132 PRACTICAL ELECTRICITY. 

By Formula (38) total internal resistance = — = — r = = ohm. 
J nq 10 5 

r = 2 ohms, nq=10 cells. 

Exp. 46 : Connect a very large Daniell cell to a low resistance galva- 
nometer and record the deflections (say 60). Now join a much smaller 
similar cell to the same galvanometer and the deflections are much 
less (say 20). The pressure is the same in both cases, but the inter- 
nal resistance of the small cell is higher, and since C = E -5- R + r 
(Formula 31), the current and the deflections must be less. Connect 
3 of the smaller cells in parallel, Fig. 112, and to the galvanometer, 
and the deflections are now equivalent to the one large cell. 
The pressure is no higher since the cells are in parallel, therefore 
the total internal resistance of the three cells must be equal to the 
one large cell, since the current and pressure are the same. 

146. Current from Cells in Parallel or Multiple.— To 

FIND THE CURRENT THAT WILL BE MAINTAINED IN A CIRCUIT 
FROM A NUMBER OF SIMILAR CELLS JOINED IN PARALLEL : 

Find the total internal resistance of the cells in parallel by 
Formula {88). Divide the E. M. F. of one cell by the sum of the 
external and internal resistances (according to Ohm's Law). 

Let E = E. M. F. of one cell; 

r = internal resistance of one cell; 

— = total internal resistance of the cells in parallel; 

R = the total external resistance. 
Then, 

^Tr (39) - 

nq ' 

Prob. 45 : Ten Daniell cells are joined in parallel and to an exter- 
nal resistance of 10 ohms. E. M. F. of 1 cell = 1 volt. Internal re- 
sistance of 1 cell = 2 ohms. Find the current through the external 
circuit. 

By Formula (39) C = — - — =-^-i — =.09 ampere. 

nq 10 

E = 1 volt, r = 2 ohms, nq = 10 cells, R = 10 ohms. 

By comparison with Prob. 43, it will be noted that with this par- 
ticular external resistance the series arrangement of the cells is much 
better, as nearly four times the current flows through the circuit when 
the cells are in series as when connected in multiple. 

147. Advantage of Parallel Connection. — Cells are con- 
nected in parallel when it is desired to obtain the maximum 



OHM'S LAW AND BATTERY CONNECTIONS. 133 

current through a low external resistance circuit, or when a 
small current is required for a long period of time. When so 
grouped the cells are equivalent to one very large cell, and 
are arranged to give a large quantity of electricity. When 
connected to a low external resistance, as compared with the 
internal resistance, the strength of current will also be large, 
while with a high external resistance the current will be 
small. The total quantity of electricity available from the 
supply of the chemicals can thus be used rapidly or slowly, 
as economy may demand. The following problems will 
illustrate this case : 

Prob. 46: What current will flow through a resistance of .1 ohm 
from a Leclanche cell of 1.4 volts E. M. F. and an internal resistance 
of .4 ohm ? 

E 14 

By Formula (31 ) C = j£q—j. = i 4- 4 = 2 - 8 amperes. 

E = 1.4 volts, R = .1 ohm, r = .4 ohm. 

Prob. 47 : What will be the current in Prob. 46 with ten such cells 
in parallel ? 

By Formula (39) C = T ^— = -~- = -q^j = 10 amperes. 

r^ + R T0 + ' 1 
E = 1.4 volts, r — .4 ohm, nq = 10 cells, R = .1 ohm. 

Prob. 48 : Suppose the ten cells in Prob. 47 are connected in series. 
What current will flow through the circuit? 

B y Formu.a (37) O= (7 f^_ = _1^0_ = 14 ^ 

amperes. 

E = 1.4 volts, ns = 10 cells, r = .4ohm, R = .lohm. 

The parallel grouping is therefore preferable in the above problems 
if the greatest possible current strength is desired in the external 
circuit. 

148. Advantage of Series Connection.— A series group- 
ing is employed when the external resistance is the principal 
one to be overcome and the maximum current strength is de- 
sired in the circuit. The advantage of this method will be 
shown by the following problems : 

Prob. 49 : A Leclanche cell, 1.4 volts and internal resistance of .4 
ohm, is connected to an external resistance of 100 ohms. What cur- 
rent will flow through the circuit? 

By Formula (31) C = ^ = ^^ = ^ = .01394 ampere. 
E = 1.4 volts, R = 100 ohms, r = .4 ohm. 



134 PRACTICAL ELECTRICITY. 

Prob. 50 : Connect ten similar cells in parallel in Prob. 49 and find 
the current. 

By Formula (39) C= E = - , L4 == jkno. = 013994 ampere. 
JL+R ^+100 1UU ' U4 
nq 10 

E = 1.4 volts, R = 100 ohms, r = .4 ohm. 

Ten cells so connected to this external resistance are, therefore, not 
much better than one cell. Compare with Prob. 44, where the ex- 
ternal resistance was very low. 

Prob,. 51 : Connect the cells in Prob. 50 in series and find the cur- 
rent strength. 

t> ^ i /o7\ n EX ns 1.4 X 10 14 

By Formula (37) C = (rXns) + R = (.4 X 10) + 100 = 104 = 

.13 ampere. 

E = 1.4 volts, ns = 10 cells, r = .4 ohm, R = 100 ohms. 

With the cells in series ten times the current is passed through this 
resistance as when the cells are connected in parallel. In ]f 146 the 
multiple combination proved to be best adapted for a particular 
circuit, while in this case the series grouping is desirable. The stu- 
dent should make a thorough comparison of the problems in ^ 146 
and 147. 

149. Cells Grouped in Multiple- Series. — A combination 
of the series and multiple grouping of cells is sometimes de- 
sirable when a number of cells are available, to give either 

the maximum current 
y— st y~jtf 7T~|nJ" TTTv" through an external 

—ft 17^ J/^l/ vj/^ resistance, or to in- 

crease the capacity of 
the cells for maintain- 
ing a current in a cir- 
cuit for a long period 
of time. For example 
8 volts E. M. F. is re- 
quired to light a small 



4QHQRW 



Fig. I13.-Multiple-Series Grouping of Cells. \ 3im ^ an d 8 cells are 

Four cells in series, two groups in parallel. Total „ Vfl jl„Ul p with an 

E. M. F. equal to that of one group. Total dVdlldUie Willi ail 

internal resistance equal to one-half J] # ]yf < p\ of 2 volts 

that of one group. ' , .' 

each. Arrange one 
group of 4 cells in series which will give the desired E. M. F. , 
8 volts *. Suppose this group would cause the lamp to burn 
4 hours. Arrange a second group of 4 cells in series and join 
this group in multiple with the first group, Fig. 113. The 
total E. M. F. is still 8 volts, but with two groups in parallel 

* Neglecting the internal resistance. See V 226. 



OHM'S LAW AND BATTERY CONNECTIONS. 135 



the quantity of electricity available has been doubled, so that 
the lamp will now burn 8 hours. Such a grouping of cells is 
called a multiple-series combination (practically a multiple of 
series). Two cells, each having an E. M. F. of 8 volts and an 
internal resistance of four times one of the above cells, could 
be placed in multiple and substituted for the 8 cells. 

To FIND THE CURRENT FROM A MULTIPLE-SERIES ARRANGE- 
MENT OF CELLS JOINED TO AN EXTERNAL RESISTANCE : 

Compute the E. M. F. and internal resistance of one group by 
Ohm's Law (Formula 37). 

Consider the results as the data for one cell and then make cal- 
culations for the number 
of such cells (groups) 
arranged in parallel (by 
Formula 39). 

Prob. 52 : A multiple- 
series combination of 8 
cells is joined to an ex- 
ternal resistance of 3 
ohms. The cells are 
arranged 4 in parallel, 2 
groups in series, Fig. 
114. Each cell has an 
E. M. F. of 2 volts and 
an internal resistance of 
.5 ohm. What current 
will flow through the ex- 
ternal circuit ? 

E. M. F. of 1 group = 2 volts. 

E. M. F. of 2 groups in series = 2 X2 = 4 volts. 

By Formula (38) Internal resistance of 1 group — — =~± = 

.125 ohm. 

E = 2 volts, nq = 4 cells in 1 group, r = .5 ohm. 

By Formula (36) Internal resistance of 2 groups in series = r X 
ns = .125 X 2 = .25 ohm. 

r of 1 group = .125 ohm, ns = 2 groups. 
E 4 

By Formula (31) C = j^q-p = 3 -j- .25 = L23 am P eres - 

R= 3 ohms, r of 2 groups in series = .25 ohm ; E= 4 volts, 2 
groups in series. 

150. Internal Resistance of any Combination of Cells. — 

To FIND THE INTERNAL RESISTANCE OF ANY MULTIPLE- 
SERIES COMBINATION OF CELLS : 

Multiply the resistance of one cell by the number of cells in one 




Fig. 114.— Series-Multiple Grouping of Cells. 

Four cells in parallel, two groups in series, equivalent 

to two cells in series and four groups in parallel. 



186 PRACTICAL ELECTRICITY. 

group and divide the product by the number of groups in multiple. 
The number of cells in each group must be the same. 
Let r = resistance of one cell; 

ns = number of cells in series in one group; 
nq = number of groups in parallel. 
Total internal resistance of any combination of cells = 

r _>lIL s (40). 

nq 

Prob. 53 : Find the internal resistance of a combination of 24 cells 
arranged 6 in series, 4 groups in multiple. Each cell has a resistance 
of 4 ohms. 

r X ns 4x6 

By Formula (40) Total resistance — = — j — = 6 ohms. 

r = 4 ohms, ns = 6 cells in one group, nq = 4 groups in multiple. 

151. Current Strength from Any Combination of Cells. 

TO FIND THE CURRENT THAT WILL BE MAINTAINED IN AN 

EXTERNAL CIRCUIT FROM ANY MULTLIPLE-SERIES COMBINA- 
TION: 

Divide the total E. M. F. of one series group by the sum of the 
combined internal and external resistances. 
Let C = Current in external circuit; 
E = E. M. F. of one cell; 
ns = number of cells in series in one group; 
nq = number of groups in parallel; 
r == internal resistance of one cell; 
R == external resistance. 
Then by Ohm's Law, Formulas (37) and (39), 

P EXns 

C = n^xTTi C41). 

nq 

Prob. 54 : Find the current that would flow through an incandescent 
lamp, hot resistance 2 ohms, when connected to 24 cells arranged 4 
in series and 6 in parallel. Each cell has an E. M. F. of 2 volts and 
an internal resistance of 3 ohms. 

By Formula^!) = 5i |^-= 4 -|fi-=| =2 amperes. 

E = 2 volts, ns =4 cells in one group, r = 3 ohms, nq— - 6 groups 
in parallel, R = 2 ohms. 

152. Cells in Opposition. — When two cells are joined in 
parallel their E. M. F.'s are in opposition, since each one tends 



OHM'S LAW AND BATTERY CONNECTIONS. 137 

to send a current through the other. If the E. M. F.'s are 
equal no current will flow through the connecting wires. Two 
equal forces, acting in direct opposition, produce equilibrium ; 
if, however, the forces are unequal, then motion is produced 
in the direction of the greater force. For example, if the 
pressure acting downward on each piston in tank A and B, 
Fig. 109, is the same, no water will flow through the con- 
necting pipe. Suppose the total downward pressure on A is 
10 pounds and on B 30 pounds, then a current of water will 
flow from B to A, due to the difference in pressure between 
the opposing forces, 20 pounds (30 lbs. — 10 lbs). The 
piston at A will move upward. When two cells of unequal 
E. M. F.'s are connected in opposition a current will flow 
through the connecting wires and internal resistance in the 
direction of the higher E. M. F. 

To FIND THE CURRENT IN ANY CIRCUIT WHEN THE E. M. 
F.'S ARE IN OPPOSITION : 

Divide the difference between the E. M. F.'s by the sum of the 
external and internal resistances. 

The opposing E. M. F. is called the Counter E. M. F. and 
is usually represented by &. 

E 

Formula (31) C =■ -p ■ may include the above state- 
ment when expressed thus C = -n _■_ • 

Prob. 54- A : Four Daniell cells, each having an E. M. F. of 1 volt 
and internal resistance of 2 ohms, are connected in series and in oppo- 
sition to an accumulator having an E. M. F. of 2 volts and an internal 
resistance of .05 ohm. The resistance of the connecting wire is 0.2 
ohm. What is the charging current? 

By above Formula C = |=| = . 2+ (4^2) + .05 = " 24 ampere ' 
E. M. F.= E X ns = 1 X 4 = 4 volts, 8 = 2 volts, r = rXns = 2X4 
= 8 ohms + .05 = 8.05 ohms, K=.2ohm. 

QUESTIONS. 

1. An electromagnet connected to a Leclanche cell attracts many 
more filings than when it is connected to a Daniell cell. Why ? 

2. Upon what factors do the E. M. F.'s of a battery and dynamo de- 
pend? 

3. An incandescent lamp receives insufficient current to properly 
illuminate it. Why is this, and what is necessary in order that it may 
burn at candle power ? 



138 PRACTICAL ELECTRICITY. 

4. A lamp requiring 4 volts is connected to two bichromate cells of 
2 volts E. M. F. each, joined in series. It fails to light properly, 
though the E. M. F. of the two cells is 4 volts. Why is this? 

5. A small size Daniell cell deflects a galvanometer 40 degrees, 
while a larger one of the same type produces 55 deflections. Why is 
this, since the E. M. F. of the cells is the same? 

6. The cells in question 5, when connected to another galvanome- 
ter, both indicate the same deflection How do you account for this? 

7. Two Partz cells are connected in series and to a large electro- 
magnet ; there are apparently no more filings attracted to the magnet 
than when one cell was used. If the iron is not nearly saturated, 
why is this, since the E. M. F. has been doubled ? 

8. Two Edison-Lalande cells are connected in parallel and to a gal- 
vanometer. The deflection is much greater than when only one cell 
was connected. Give reasons, since the E. M. F. is the same in both 
cases. 

9. A Bunsen cell has an E. M. F. of 2 volts and an internal resist- 
ance of .4 ohm. Why will not this cell give 7 amperes through a very 
low external resistance? 

10. If you are given the choice of two small Daniell cells or one 
large Daniell cell of twice the capacity of the small ones, which would 
you prefer ? Why ? 

11. Would you connect two cells having an E. M. F. of 0.7 and 2.4 
volts respectively in series ? Give a reason for your answer. 

12. Would you connect the cells mentioned in question 11 in par- 
allel? Give reason for your answer. 

13. The zinc rods of two Fuller cells are connected by a wire, 
and wires are led from the two carbon terminals to a galvanometer. 
The cells are in good condition and the connections tight, but the 
needle is not deflected. Give reason and illustrate your answer by 
a sketch. 

14. If you are asked to select a good open circuit cell, what require- 
ments should it fulfill? 

15. The voltage applied to the terminals of a lamp is to be doubled, 
but the lamp must not receive any more current than before. Ex- 
plain how this could be accomplished. 

PROBLEMS. 

1. What pressure must be applied to an incandescent lamp if it 
has a resistance of 55 ohms and requires 2.2 amperes ? Ans. 121 volts. 

2. A Daniell cell has an E. M. F. of 1 volt and an internal resistance 
of 2.2 ohms. What current will flow through an electromagnet con- 
nected to it, wound with 150 feet of No 18 B. & S. copper wire? Ans. 
0.312 ampere. 

3. The current through the field magnets of a dynamo is 2 amperes 
and the applied pressure 120 volts. What is the resistance of the 
circuit? Ans. 60 ohms. 

4. The E. M. F. of a cell is 2.44 volts, its internal resistance .6 
ohm, and it is connected to a circuit of 1.4 ohms. What pressure is 
required to send the current used through the battery ? Ans. 0.732 
volt. 



OHM'S LAW AND BATTERY CONNECTIONS. 139 

5. A bell circuit is operated by 3 Leclanche cells in series. Each 
cell has an E. M. F. of 1.4 volts, and an internal resistance of .4 ohm. 
What current will the bell receive if its resistance, including the line, 
is 20 ohms? Ans. 0.198 ampere. 

6. To operate a small motor 6 Grenet cells are connected in par- 
allel. Each cell has an E. M. F. of 2 volts and an internal resistance 
of .6 ohm. The total external resistance is .9 ohm. What current 
will the motor receive ? Arts. 2 amperes. 

7. Some miniature incandescent lamps are lighted by 24 Edison- 
Lalande cells, arranged 4 in series and 6 groups in parallel. Each 
cell has an E. M. F. of .7 volt and an internal resistance of .15 ohm, 
and the external circuit has a resistance of .21 ohm. What current 
do the lamps receive? Ans. 9 amperes. 

8. Four Leclanche cells, E. M. F. 1.4 volts each, and internal 
resistance of .4 ohm each, are to operate an electric gas igniting cir- 
cuit of 15 ohms resistance. Would you connect the cells in series or 
in parallel? Prove your answer by calculation. Ans. 0.337 ampere. 

9. Calculate the current from all symmetrical combinations of 6 
cells connected to an external resis tance of 2 ohms. Each cell has an 
E. M. F. of 1.4 volts and an internal resistance of .5 ohm. Ans. Series = 
1.68 amperes ; parallel = .67 ampere ; 2 in series, 3 groups in parallel = 
1.2 amperes ; 3 in series, 2 groups in parallel = 1.52 amperes. 

10. A Harrison cell E. M. F. 2.5 volts, internal resistance .4 ohm 
and a dry cell 1.5 volts and .6 ohm internal resistance are connected 
in parallel. What current will flow through the connecting wire? 
Ans. 1 ampere. 

11. A Daniell cell, Grenet cell, and Leclanche cell having E. M. F.'s 
of 1.1, 2, and 1.4 volts and internal resistances of 2.0, 0.3, and 0.5 ohms 
respectively, are connected in series to a resistance of 3 ohms. What 
current flows through the external resistance? Ans. .77 ampere. 

12. Eight cells are joined in series-multiple ; 4 cells in multiple, 2 
groups in series, Fig. 114. Each cell has an E. M. F. of 2 volts and 
an internal resistance of .5 ohm. The cells are connected to a small 
incandescent lamp having a hot resistance of .75 ohm. What current 
will the lamp receive ? Ans. 4 amperes. 



LESSON XIV. 

CIRCUITS AND THEIR RESISTANCE. 

Conductance of a Circuit — Resistances in Series— Equal Resistances in 
Parallel (Joint Resistance) — Unequal Resistances in Parallel — 
Conductivity Method for Conductors in Parallel — Resistances 
Joined in Multiple-Series— Division of Current in a Divided 
Circuit — Potential Difference in Multiple Circuits— Current in 
Branches of Multiple Circuits — Shunts — Rheostats— Resistance 
of Connections— Laboratory Rheostats — Table X. Resistance of 
Commercial Apparatus — Questions and Problems. 

153. Conductance of a Circuit. — The Conductance of a 
Circuit is the Reciprocal of its Resistance. (The recip- 
rocal of a number is the quotient obtained by dividing one 

1 2 3 1 

by that number, as the reciprocal of 4 = ^ ; of ^ = ?> = l^- ) 

The unit of conductance is the mho (ohm spelled backward). 
A wire of 1 ohm resistance has a conductance of 1 mho ; if of 

2 ohms resistance, „ mho ; 8 ohms resistance, g mho ; -g ohm 

resistance, g or 1^ mhos. The resistance of a circuit is the 
reciprocal of its conductance. A wire of 7 mhos conductance 
has -- ohm resistance. If in Ohm's Law, conductance is 
used instead of resistance, and K represents the conductance 
of a circuit in mhos. 
Then, 

C = EXK; 

K = § .(42). 

154. Resistances in Series. — To find the total resist- 
ance OF A NUMBER OF RESISTANCES CONNECTED IN SERIES : 

Find the mm of the resistances connected. In Fig. 115, A equals 
40 ohms; B equals 160 ohms; total resistance equals 
40 -f 160 = 200 ohms. The same current will flow through 
A as through B. 
140 



CIRCUITS AND THEIR RESISTANCE. 



141 



155. Equal Resistances in Parallel— Joint Resistance. 

In Fig. 116 the two resistances, A and B, are connected in 
parallel, and then in series with the battery wires. If the re- 
sistance of A is equal to that of B, the conductance will also 
be equal and the current will divide, one- half flowing through 

A and the other half through 



t — ^ 



Fig. 115. 



-Two Unequal 
in Series. 



^— > 



Resistances 



B B. Since the total area of the 

conducting circuit has been 
increased, the combined or 
joint resistance of A and B 
will be less than either re- 
sistance separately. If the 
resistance of A equals that 
of B then the area will have 
been doubled, and the joint resistance equal to one- 
half that of A or B. Thus A and B == 10 ohms each ; 

joint resistance = k of 10 or 5 ohms. With three equal re- 
sistances in parallel the joint resistance will be g the value of 
one of the resistances. 

To Find the Joint Resist- 
ance of any Number of 
Equal Resistances Connec- 
ted in Parallel : 

Divide the value of a single 
resistance by the number con- 
nected in parallel. 

Let R = a single resistance ; 
nq:= number of equal 
resistances in parallel; 
J. R. = joint resistance. 




Fig. 116. — Two Unequal Resistances 
in Parallel. 



Then, J. R. = 



R, 

nq 



(43). 



To Find the Number of Equal Resistances Connected in 
Parallel (nq) When the Joint Resistance (J. R.) and 
Value of a Single Resistance (R) Are Known : 

Divide the value of a single resistance by the joint resistance. 



Thus, 



R 
nq =jTR 



(44). 



142 



PRACTICAL ELECTRICITY. 



To Find the Value of a Single Resistance (R) When 
the Joint Resistance and the Number of Equal Resist- 
ances in Parallel are Known: 

Multiply the joint resistance by the number of equal resistances 
connected in parallel. 



R = J. R. x nq 



(45), 



oJ 



:wmmm 



Prob. 55 : Ten incandescent 
lamps are connected in parallel, 
Fig. 117. Each lamp has a re- 
sistance (hot) of 220 ohms. 
What is the total or joint re- 
sistance of the lamp circuit? 

By Formula (43) 

T ^ R 220 00 , 
J.E. = -=- I6 - = 22ohm B . 

R = 220 ohms, nq = 10 lamps in parallel. 

Prob. 56 : The joint resistance of 55 lamps connected in parallel is 
4 ohms. What is the resistance of 1 lamp ? 



Fig. 117.— Ten Incandescent Lamps Con- 
nected in Parallel and to a Dynamo. 



By Formula (45) R 
J. R. 



J. R. X nq — 4 X 55 = 220 ohms. 
4 ohms, nq =55 lamps. 

Prob. 57 : The joint resistance of a number of electromagnets con- 
nected in parallel is 8 ohms and the resistance of 1 magnet, 40 ohms. 
How many magnets are connected ? 

By Formula (44) nq = Y-p-=-r =5 electromagnets. 



R 



J. R. 8 

40 ohms, J. R. 



ohms. 




3 OHM 5 

, "W 



7 0HM6 

* IW ' 



156. Unequal Resistances in Parallel. — In Fig. 118, two 
unequal resistances, 3 and 7 ohms respectively, are connected 

in parallel. The joint re- 
sistance will be less than 
either resistance considered 
separately. 

To Find the Joint Re- 
sistance of Two Unequal 
Resistances Connected in 
Parallel : 

Divide the product of the 
resistances by their sum. 

Let R = first resistance ; 
R,= second resistance ; 

J. R. — joint resistance. 



Fig. 118. — The Joint Resistance of 

Two Unequal Resistances 

in Parallel. 



CIRCUITS AND THEIR RESISTANCE. 143 

Then the joint conductivity = = _|_ i — ^i+^mhos, 

l\ ^ Jtt X -tii 

and the joint resistance = 1 ^§L±_^ =: |_^A hms, 

it X Jtij K -f- Kj 

or J. R. = ?_><ik (46). 

R 4--Rj 

Prob. 58: Find the joint resistance of two coils in parallel, having 
a resistance of 3 and 7 ohms respectively. Fig. 118. 

By Formula (46) J. R. = |*Lg, = 3j<_7 = ^ ohmg 

R = 3 ohms, Rj = 7 ohms. 
If more than two Unequal Resistances Are Connected 
in Parallel : 

First find the joint resistance of two wires, and considering this 
as a single resistance, combine it with a third resistance, and so on. 

157. Conductivity Method for Conductors in Parallel. 
To Find the Joint Resistance of any Number of Resist- 
ances Connected in Parallel : 

Find the sum of the conductivities of the different paths through 
which the current flows and the joint resistance ivill be the recip- 
rocal of the sum thus obtained. 

Prob. 59 : Find the joint resistance of 2 coils having 3 and 7 ohms 
resistance respectively, Fig. 118, by the conductivity method. 

B „.„.., 1.1 7 + 3 10, 

By ]| 157 joint conductivity =•«- + ^ = ~n\ — ~ oT mho. 

21 
Joint resistance = y~ =2.1 ohms. 

Compare with Problem 58. 

Prob. 60 : Find the joint resistance of 3 coils of wire having re- 
sistances of 2, 4 and 8 ohms respectively, Fig. 119. 

By fl 157 joint conductivity =•« + ~Z +~q = g == ~a m ho. 

g 
Joint resistance = -= == 1.142 ohms. 

158. Resistances Joined in Multiple -Series. — The same 
method of calculation is used as that already given for the 
internal resistance of cells, ^J 145. 

When the Resistance of all the Series Groups are the 
Same : 

Find the resistance of one group, and divide this sum by the 
number of groups in parallel. 



144 



PRACTICAL ELECTRICITY. 



SOHMS 



When the Groups are of Unequal Resistance : 
Find the sum of the series resistances in one group, and treat- 
ing this as a single resistance proceed as in ^j 157. 

159. Division of Current in a Divided Circuit. — The 

division of current in the branches of a multiple circuit is directly 
proportional to the conductance of the branches, or inversely pro- 
portional to their resistance. 

If A and B, Fig. 116, are equal in resistance and a cur- 
rent of 12 amperes flows from the battery, 6 amperes will 

flow through A, and 6 am- 
peres through B. If A has 
a higher resistance than B 
(and consequently a lower 
conductance) , then the greater 
portion of the current will 
flow through the lower re- 
sistance of B (which has a 
higher conductance.) 

If A has 2 ohms resistance 
and B 1 ohm, then twice as 
much current will flow 
through B as through A ; or 
the current is divided into three parts, one- third of which 
flows through A and two-thirds through B. If the total cur- 
rent is 12 amperes, A then receives 4 amperes and B 8 amperes. 

Prob. 61 : A current of 39 amperes is passed through 3 coils of wire 
joined in multiple, Fig. 120, having the following resistances : A = 8, 
B = 12, and C = 16 ohms respectively. How many amperes will each 
coil receive? 

By ff 157 joint conductance = \ + l ' 



1 «t« — ' 



Fig. 119. 



-Three Unequal Resistances 
in Parallel. 



The conductance of A 



12 
mho, of B 



48 



13 , 
= 48 mha 



— mho, and of C = -^ mho. 

48 48 



Consider the current to divide into 13 parts (6 + 4 + 3), 6 parts of 
which pass through A, 4 through B, and 3 through C, or directly 
as their conductances. 



Current through A == jo of 39 = 18 amperes ; 
4 



B 

C 
Total current, 



13 



of 39 = 12 amperes ; 

of 39 = 9 amperes. 
.... 39 amperes. 



CIRCUITS AND THEIR RESISTANCE. 145 

160. Potential Difference in Multiple Circuits. — The 
Potential Difference Required to be Maintained Be- 
tween the Points where Several Circuits Branch and 
Where They Again Unite, is 
equal to the sum of the currents A o ohms 

in all the branches, multiplied 
by the joint resistance of the 



(x/xtx/xtlTi 

0/WJTJUlflJl 
C 16 oUs 



branches. 39Amp». 

E= potential difference across 

branches ; C, C 15 C 2 , etc. = cur- n/UUlMilW 

rent in the branches ; J. R. = Fig. 120.— Finding the Current 

ioint resistance of the branches, Strength through the Branches 

•L. iHr . of a Divided Circuit. 

Fig. 119. 

E=.(C + C x + C 2 ;etc.) X J. R (47). 

Prob. 62 : Three coils, A, B, and C, have a resistance of 8, 12, and 

16 ohms respectively. Find the potential difference required to send 

18 amperes through A, 12 amperes through B, and 9 amperes 

through C. 

13 
From Prob. (61) Joint conductance — - to mho, therefore 

Joint resistance =• y> =3.69 ohms. 

By Formula (47) E = (C + d + C 2 ) X J. R. = (18 + 12 + 9) X 3.69 
= 143.9 volts. 
C = 18 amperes, ^ = 12 amperes, C 2 = 9 amperes, J. R. =3.69 ohms. 

161. Current in Branches of Multiple Circuits.— The 

Current, in Any Branch of a Multiple Circuit, is Found, 

by dividing the potential difference between where the branches 
divide and unite, by the separate resistance of each branch. 

The separate resistances of the branches of a multiple 
circuit may be found by multiplying the current through any 
branch, .by the potential difference across the branches, ac- 
cording to Ohm's Law. 

Prob. 62-A : Find the current through each branch of the divided 
circuit in Fig. 119, if the potential difference is 24 volts. 

By1[ 161 C = ^ = | 4 = 12 amperes. 

24 24 

Also -j- = 6 amperes and -^ = 3 amperes. 

162. Shunts. — If the current passing through the galva- 
nometer G, Fig. 121, is too large, or the wire with which it is 
wound too small to carry a large current, only a small frac- 



146 



PRACTICAL ELECTRICITY. 




tion of the total current may be passed through the galva- 
nometer, the remainder passing through the wire, S, connected 
across the galvanometer terminals. The wire, S, forms a 
' ' by-path ' ' for the current, and is 
called a shunt, and the galvanometer 
is said to be shunted. If the resist- 
ance of the galvanometer is 1 ohm 
and the shunt 1 ohm, then as 
much current will flow through the 
shunt as through the galvanometer. 
If the resistance of the galvanometer 
is 2 ohms and the shunt 1 ohm, then 
twice as much current will flow 
through the shunt as through the 
galvanometer; that is, the galva- 
nometer reading must be multiplied 
by 3 to obtain the total current flow- 
ing from the battery. The value 3 is called the multiplying 
power of the shunt, that is, it is the amount by which the 
shunt multiplies the range of the galvanometer. Any galva- 
nometer (ammeter or voltmeter) may, therefore, have its 
range of indication increased by shunting it. 
Let G = galvanometer resistance ; 
S = shunt resistance ; 
C = total current in the joint circuit; 
Cg = currrent in the galvanometer circuit. 
The multiplying power of a shunt is the ratio of the total 
current flowing in the circuit, C, to that part of it, Cg, which 
flows through the galvanometer. The total current, C, bears 
the same ratio to the galvanometer current, Cg, that the sum 
of the resistances, G -f- S, bears to the shunt resistance. 
C G + S 



11. — A Shunted Galva- 
nometer. 



Thus 



or 



G 



Cg" 

f-S 



s ; 

G S G 1 

: s~+s — s + 1 - 



1. To Find the Multiplying Power of a Shunted 
Galvanometer : 

Divide the galvanometer resistance by the resistance of the shunt 

and add one to the quotient. 

P 

Multiplying power of a shunt (n) =q — {— 1 - . . (48). 




CIRCUITS AND THEIR RESISTANCE. 147 

Prob. 63 : Find the number by which the readings on a Weston 
voltmeter must be multiplied (or the multiplying power of the 
shunted galvanometer) in Fig. 122, when resistance of voltmeter (gal- 
vanometer) is 5000 ohms, and resistance of shunt placed across its 
terminals is 500 ohms. 

By Formula (48) n = J" + 1 = ^ = 10 -f 1 = 11. 

The readings are to be multiplied by 11 to obtain the true value of 
the total current flowing. 

2. To Find the Current Flowing Through a Shunted 
Galvanometer, Cg, When the Total 
Current, C, Flowing Through the M <Wwj, »* 
Circuit is Known : 

Divide the total current by the ratio 
of the galvanometer resistance to the shunt 
resistance, plus one. 

Cg = r A- (49). 

S+ 1 

,, , „, T , OA a , •, Fig. 122.— Current Through 

Prob. 64 : If 30 amperes flow from the a Shunted Galvanometer! 

battery in Fig. 122, when the galvanometer 

resistance is 5000 ohms and the shunt 500 ohms, what current will 

flow through the galvanometer? 

By Formula (49) Cg = ^~ = ^~— = IT = 2 ' 7 am Peres. 
8 +1 5W + 1 

3. To Find the Value of a Shunt's Resistance to Give 
a Certain Multiplying Power (n) : 

Divide the galvanometer resistance by the multiplying power 
desired, minus one. 

Let n = the desired multiplying power ; 
S = shunt' s resistance ; 
G- r= galvanometer resistance. 

Then, 8='^ (50). 

Prob. 65 : What must be the resistance of a shunt to give a multi- 
plying power of 100, when used with a galvanometer of 5000 ohms 
resistance? Fig. 122. 

By Formula (50) S = ^^ = 1QQ __ 1 = -^T = 50.5 ohms. 
In practice n, is generally 10, 100, or 1000. 



148 



PRACTICAL ELECTRICITY. 



These three shunt coils, calculated for any particular gal- 
vanometer, are arranged in a plug box, called a shunt box, 
similar to Fig. 125, and by withdrawing the plugs any par- 
ticular shunt can be quickly connected to the galvanometer. 
The multiplying power is stamped on the box to correspond 
with each plug. This shunt box can only be used with the 
galvanometer (ammeter or voltmeter), for which it was calcu- 
lated. Shunt boxes are sometimes called multipliers. By 
connecting a shunt across a galvanometer the resistance of 
the circuit is decreased. If it is desired to keep the resistance 
the same as when the galvanometer was not shunted, another 
resistance, known as a compensating resistance, is added in series 

with the shunted galva- 
nometer. The value of the 
resistance to be added equals 
n— 1 




G X 



n 



163. Rheostats.— The 

usual method of regulating 
and controlling the current 
required for various electri- 
cal purposes is by inserting, 
or taking out of a circuit, re- 
sistance. It will be seen, from 

Ohm's Law, C = |, that if 

the pressure (E) is constant 
the current (C) can readily 
be regulated by increasing 
or decreasing the value of 
R ; that is, changing the re- 
sistance in circuit. An adjustable resistance or any apparatus 
for changing the resistance without opening the circuit is called 
a rheostat. The function of a rheostat is to absorb electrical 
energy, and this energy, which appears as heat, is wasted in- 
stead of performing any useful work. A rheostat may be 
constructed of coils of iron wire, iron plates or strips ; car- 
bon, either pulverized in tubes or in the form of solid rods 
or discs ; German silver, platinoid, etc. , wound on spools ; 
columns of liquids, as water and mercury, etc. The cross- 
sectional area of the material must be sufficient to carry the 
current without excessive heating. In rheostats used for 



Fig. 123. 



-Commercial Type of 
Rheostat. 



CIRCUITS AND THEIR RESISTANCE. 



149 




Fig. 124. — Commercial Rheostat. 

Diagram of connections of the 
resistance coils. 



regulating the current in commercial electric circuits no great 

degree of accuracy of the resistance coils is required, as is the 

case in laboratory rheostats, ^j 165. Fig. 123 illustrates a 

commercial type of rheostat, in 
which the various coils are con- 
nected to brass buttons or con- 
tact segments. By moving a 
metallic connecting arm over 
the segments the coils are thrown 
in or out of circuit, and the re- 
sistance thus readily adjusted, 
as shown in the diagram of con- 
nections, Fig. 124. In some 
types of rheostats the wire is 
wound around an iron frame- 
work which has been previously 
dipped into a fireproof insulat- 
ing enamel. The advantage of 
this construction is that the heat 
from the wire is dissipated much 
more rapidly, so that a much 

smaller wire can be used to carry a given current. The size 

of such an enameled rheostat, required for absorbing a 

given amount of energy, is much smaller than one made 

of coils of wire 

stretched between 

an iron supporting 

frame- work. 
164. Resistance 

of Connections. — 

When two surfaces 

are pressed lightly 

together the resist- 
ance of the contact 

is much greater 

than if the surfaces 

of contact are firmly 

pressed together. 

i. .-. . b -., Fig. 125.— Laboratory Type of Rheostat. 

For this reason all 

joints in electrical conductors should be soldered to decrease 

the resistance of contact; all binding screw contacts and 

connections should be thoroughly cleaned and of a bright 





150 PRACTICAL ELECTRICITY. 

metallic color when used, and screwed down so as to clasp 
the wires firmly. 

165. Laboratory Rheostats. — For making electrical 
measurements accurately standardized resistance boxes are re- 
quired. The current passed through these rheostats is gen- 
erally a fraction of an ampere, so that the resistance wire, 
mostly German silver or platinoid, is small in size and is 
wound on spools which are contained in a case, as shown in 
Fig. 125. Brass strips are mounted on the top of the case, 
and the terminals of each coil connected to two adjacent 
strips as shown in detail in Fig. 126. The 
insertion of a tapered metal plug into a 
tapered hole formed by the adjacent strips, 
short circuits or cuts out the resistance coil. 
By removing the plugs, resistance is in- 
serted in the circuit in which the box is 

Fig- 126.— Connection connected. The accurate resistance of each 
of a Resistance Coil. ., . t ,11 i 

coil is stamped on the box, as shown m 

Fig. 234, so that the resistance in circuit is found by the 

addition of the values of the coils unplugged. The coils are 

wound non-inductively, ^j 299, and the size of the wire used 

must be such that no appreciable error will be introduced 

by the heating of the coils. 

Table X. — Eesistances of Commercial Apparatus. 

GALVANOMETERS. 

Thomson mirror galvanometer, 1 ohm to 350,000 ohms. 

" common resistance, . . . 5,000 " 

D' Arson val galvanometer, 1 ohm to 750 " 

" " common resistance, 250 " 

AMMETERS. 

Kesistance is less the larger the size of instrument required. 
Weston, 15 amperes capacity, 0022 ohm. 

VOLTMETERS. 

Cardew voltmeters for 100 volts, about, 500 ohms. 

Weston " " 150 " " 150000 " 

BATTERIES. 

Gravity cell, . . . 2 to 4 ohms. 

Leclanche, 1 

Bichromate, .4 " 

Edison-Lalande, 300 ampere-hours, .02 " 

Accumulator, 100 ampere-hours, .005 " 



CIRCUITS AND THEIR RESISTANCE. 151 



TELEGRAPHY. 

Sounders, 20 ohms. 

Neutral relays, 80 to 300 " 

TELEPHONY. 

Bell telephone, about, 75 ohms. 

Call bell, from, 75 to 1000 

Magneto armature, 500 ' ' 

Induction coil, primary, 0.28 " 

" " secondary, 12 to 160 " 

DYNAMOS AND MOTORS. 

Armature resistance (warm) .5K. W. dynamo or motor, 

about, ... 4. ohm. 

And between brushes, 3 K. W. dynamo or motor, about, 0.4 
And between brushes, 20 K. W. dynamo or motor, 

about, 0.025 

And between brushes, 100 K. W. dynamo or motor, 

about, 0055 

And between brushes, 200 K. W. dvnamo or motor, 

about, " 0024 " 

ALTERNATING CURRENT TRANSFORMERS. 

0.5 K. W. capacity, primary, 21.8 ohms, secondary, .04 ohm. 
2. " " " ' 5.5 " " .015 " 

20. " " " 0.48 " " .0015 " 

INCANDESCENT LAMPS. 

At 52 volts, a 16 candle-power lamp (hot), 48 ohms. 

a (I a it 9 1 il i ' 

"110 " "10 " 

" " " "16 " 

" " " "24 " 

" " " "32 " 

" " " "50 " 

HUMAN BODY. 

The resistance of the human body varies widely with the position 
of electrodes, their area, the dryness of the skin, the duration of ap- 
plication, and the current strength. A very low resistance recorded, 
was 214 ohms from surface of head to surface of right calf, and 500 
ohms from hand to hand, each immersed to the wrist in salt water. 
Average resistance under latter conditions, 1000 ohms. 

QUESTIONS. 

1. The arc lamps connected to a series dynamo are joined in series 
with it. How is the resistance of the circuit affected as additional 
lamps are inserted in the circuit ? 

2. What is a shunt ? What advantages does it possess when used 
with a galvanometer ? 

3. A number of incandescent lamps are connected in multiple and 
to a dynamo. How will the resistance of the circuit be affected if 
one lamp is turned off ? 



wer lamp ^noij, . . 


. . . . <±o 
.... 32 


l u 11 


... .343 


C ti it 


.... 215 


i a a 


.... 144 


i a a 


.... 107 


i a u 


.... 69 



152 PRACTICAL ELECTRICITY. 

4. What advantage does an enamel type of rheostat possess over 
one constructed in the ordinary manner ? 

5. State for what uses laboratory and commercial types of rheostats 
are designed, and also the essential differences between them. 

6. An electric heater consists of coils of iron wire through which a 
current of 2.5 amperes flows, when joined in parallel with an incan- 
descent lamp which receives one ampere ? Which object possesses 
the higher resistance ? Give proof for answer. 

7. If a joint in an electrical current is mechanically stronger than 
the wire of which it is made, why should it be necessary to solder it? 

8. Two resistances, A and B, having 3 mhos and 1.5 ohms re- 
spectively, are connected in parallel and to a source of current. 
Which one will receive the greater current? 

PROBLEMS. 

1. Four hundred incandescent lamps are connected in parallel to a 
dynamo circuit. Resistance of the line .5 ohm and hot resistance of 
1 lamp 220 ohms. Potential difference at dynamo terminals 112 volts. 
What current flows through the circuit ? Give sketch. Ans. 106.66 
amperes. 

2. What length of No. 24 B. & S. copper wire would have an 
equivalent resistance to the joint resistance of 2 lamps connected in 
parallel? One lamp has a resistance of 110 ohms, the other 33 ohms. 
Give sketch. Ans. 950.27 feet 

3. Three copper electroplating baths are connected in parallel and 
to a dvnamo which furnishes 117 amperes to them. The resistance 
of the baths is, No. 1, 24 ohms ; No. 2, 36 ohms ; No. 3, 48 ohms. What 
current does each bath receive ? Give sketch. Ans. 54 ; 36 ; 27 
amperes. 

4. What potential difference must be maintained across the multi- 
ple circuit in Prob. 3? Ans. 1296 volts. 

5. Sketch and name six combinations of 4 incandescent lamps con- « 
neeted to a pair of supply lines. Each lamp has a resistance of 220 
ohms (hot) and the potential across the mains is 110 volts. What 
current will each combination receive? Ans. .125; 2, .5; .2; .376; 
.3 amperes. 

6. In a trolley car, 5 lamps, each requiring } ampere and 100 volts, 
are connected in series and between the line and track across which 
500 volts potential is maintained. If 10 cars wired as above were run- 
ning, what would be the joint resistance of the lamp circuit and how r 
much current would flow from the power station ? Ans. 100 ohms 
J. R. ; 5 amperes. 

7. The resistance of an ammeter shunt is 0.2 ohm and the instru- 
ment with its leads 24 ohms. What pressure is required to send 10 
amperes through the joint resistance of the ammeter and its shunt in 
parallel? Ans. 1.9 volts. 

8. How much of the current flows through the ammeter in 
question 7? Ans. .082 ampere. 

9. What is the multiplying pow r er of the above shunt ? Ans. 121. 
10= Two electromagnets of 8 and 20 ohms respectively are joined 

in parallel. If 10 amperes flow through the 8-ohm magnet, what 
current does the 20-ohm magnet receive? Ans, 4 amperes, 



LESSON XV. 



ELECTROMAGNETISM. 



Electromagnetism — Direction of the Lines of Force of a Straight 
Current-Carrying Wire— Deflection of a Horizontal Magnetic 
Needle — Right- Hand Rule for Direction of Whirls — Right-Hand 
Rule for Direction of Current or Deflection of Needle — Magnetic 
Field of a Circular Wire Carrying a Current — Magnetic Field at 
the Centre of a Circular Current— Magnetic Polarity of a Circular 
Current— The Helix and Solenoid— Testing the Polarity of a 
Solenoid — Rules for Determining the Polarity of a Solenoid — 
Graphical Field of a Solenoid — Questions. 

166. Electromagnetism. — 

Exp. 47 : Connect three or four chromic acid cells in parallel, close 
the circuit through a heavy bare copper wire, and then plunge the 
wire into iron filing?. The filings 
are attracted to all sides of the 
wire, as though it were a magnet. 
Any part of the wire will attract 

Iron Filings 




Battery 

Fig. 127. — A Current-Carrying 

Wire Attracting Iron 

Filings. 

the filings when the current is 
flowing, and the attraction will 
be equal on all sides of the wire, 
Fig. 127. When the circuit is 
broken the filings drop off of the 
wire. 

Electromagnetism, as distin- Fig. 128.— Graphical Magnetic Field of 
guished from magnetism in a a Current-Carrying Wire. 

permanent steel magnet, is the Made by irou fllings - 

magnetism produced around a conductor when a current floivs 
through it, A current of electricity is defined, in part, as the 

153 




154 



PRACTICAL ELECTRICITY. 




Fig. 129. — Magnetic Whirls of a Current-Carrying Wire, 
near the wire. The magnetic field of the wire 



magnetic field set up around a current-carrying conductor. 

Every wire carrying a current possesses this magnetic field, 

which fact 
can be 
proved by 
bringing a 
compass 
needle 
acts on the 

magnetic field of the compass needle, and it is deflected. 

Exp. 48 : Pass a heavy copper wire vertically through the centre 
of a piece of cardboard held horizontally, upper view of Fig. 128, and 
send a strong current through the wire. Tap the card while sift- 
ing filings upon it, and they arrange themselves in concentric circles 
around the wire and at right angles to it. The plan view of Fig. 128 
illustrates a graphical field made in this manner. By using paraffin 
paper the field may be fixed by applying heat. 

The filings are magnetic bodies free to move, and arrange 
themselves in the circular direction of the magnetic lines of 
force surrounding the wire. A compass needle held near the 
wire will take up a position tangent to the circular field at 

any point, whether the cur- ; ^ 

rent be passed up or dow r n 
the wire. The magnetic 
field, around a straight wire 
carrying a current, consists 
of a cylindrical whirl of cir- 
cular lines, their density de- 
creasing as the distance from 
the wire increases, as illus- 
trated in Fig. 129. The cir- 
cular lines of force, or mag- 
netic whiiis, do not merge 
into, cross, or cut each 
other, but complete their cir- 
cuits independently around 
the wire. 

167. Direction Of the Fi S- 130.-Current Flowing Up-Whirls 
_ . „ - « Anti-Clockwise. 

Lines of Force of a ■- t 

C+v.oi/vli+ n 11T .» flT1 + r'awcr The compass needles on the horizontal card- 
Dll dlgnt LfUrreilfc-Odl I y- board arrange themselves in the direction 

inff Wire of tlie current ' s field. 

Exp. 49 : Pass a wire vertically through a sheet of cardboard held 
horizontally. Arrange a number of poised needles or compasses 




ELECT R OMA GNETISM. 



155 



around the wire in the form of a circle, Fig. 130, of such diameter 
that all the needles point nearly N and S. Pass a strong current 
through the wire from a battery'so that the current flows up, or to- 
ward you as you look down upon the cardboard. 

When the current flows up 
through the wire, Fig. 130, 
the needles, being magnetic 
bodies, arrange themselves 
around it in the direction of 
the circular lines of force, 
also so that the needles' 
magnetic lines of force are 
in the same direction as the 
magnetic lines of the circu- 
lar field, <j\ 43. The N-poles 
of the needles point in the 
same direction as the mag- 
netic lines of the current, 
and these lines pass through 
each of the needles, entering 
at the S-pole and emanating 
at the N-pole. The direc- 
tion of the field with the current flowing up is left-handed, 
or opposite to the direction in which the hands of a watch 





I 


~ \ 


I 




r i ($ 


1 I 







&0 "1 


i 




i 

v. 

131.- 




Fig 


—Current Flowing Down- 
Whirls Clockwise. 




o 

Win 




Wm 



X 



sl^lll^N 






Fig. 132. — Direction of Whirls when Fig. 133. — Direction of Whirls when 

the Current Flows Toward You — the Current Flows Away from 

Anti-Clockwise. You — Clockwise. 

would move, as shown in Fig. 130 and also 136, where 
the wire is supposed to be passed through the watch with the 



156 



PRACTICAL ELECTRICITY. 



current flowing toward you as you look at its face. Reverse 
the direction of the current so that it now flows down through 
the cardboard, or along the wire in the same direction that 
you are looking. The needles now reverse their direction, 
and the N -poles point around the wire in the opposite direc- 
tion to what they did in the previous case, Figs. 131 and 133. 
The direction of the lines of the circular field is therefore re- 
versed, or is in the same direction as the hands of a watch 
move, Figs. 131 and 136. 

The direction of a current's circular magnetic field is the same 
as the natural direction of the magnetic lines through a poised or 
suspended needle ivhen brought under the influence of the current's 
field. The direction the needles take up around the wire, 
right-handed or left-handed, is another reason for assuming 
that a current has direction. The direction of current in any 
vertical wire can thus be determined by a single magnetic 
needle, by noting the general direction its N-pole points when 
presented near to the wire. 

If the N-pole points clockwise as you look doivn upon it the cur- 
rent is flowing from you, or in the same direction as that in which 
you are looking ; if anti-clockwise, the current is flowing toward 
you. Compare Figs. 132 and 133 with Fig. 136. 



Battery 




l y Dotted Circles and Arrovs 

\ thereon indicate direction 

~-.\.J of Current's Field of Fore: 



Fig. 134.— A Magnetic Body Free to Move, etc., *[\ 43. 



Exp. 50 : Figs. 132 and 133 show a plan view of the position of the 
needles on a horizontal piece of cardboard, with a vertical wire passed 
through it, when the current flows in opposite directions. Using a 
single compass needle, the student should verify the diagrams and 
make notebook sketches, 



ELECTR OMA GNETISM 



157 



168. Deflection of a Horizontal Magnetic Needle. — 

When a wire is held horizontally over a poised magnetic 
needle, pointing N and S (or in the magnetic meridian), Fig. 
134, and a current passed through it, the needle is deflected 
and tends to take up a position at right angles to the wire. 
When the current is sufficiently strong, the needle moves, so 
that it will accommodate through itself the greatest number 
of magnetic lines of the circular field, and also to such a posi- 
tion that its own natural magnetic lines will be in the same 
direction as the current's lines of force. 

Considering Fig. 134, the current flows over the needle from 
right to left (also N to S). As you look along the wire in the 
direction of the current the direction of the whirls is right- 
handed or clockwise, as indicated by the dotted circles in 
Fig. 134, and also on the lower diagram of Fig. 136, the N-pole 




E F G 

Fig. 135.— Resultant Deflections of the Magnetic Needle When Placed Near 
to a Current-Carrying Wire. 

of the needle, N„ moves to the position, N 2 , at right angles to 
the wire, and in the direction of the field underneath the wire 
(which is from S 2 to N 2 ), so that the direction of the whirls 
and the needle's natural lines are coincident. 

Consider the right hand, Fig. 134, as N, and the left hand 



158 



PRACTICAL ELECTRICITY. 



as S. The direction of the current's field underneath the 
wire is then from west to east, and the N-pole of the needle 
is deflected east. When a current flows from North Over a needle 
to South the N-end is deflected "East. See A of Fig. 135. This 
may be remembered by the combination of the above letters, 

which forms the 
o 






+ 



? 






t 




Aifi 



y? 



A 



m 



o 



"■ \J$ + 



Fig. 136— Clock Rule for the Direction of Whirls 
Around a Straight Wire. 



word NOSE. The 
converse of this 
statement is also 
true. If a needle 
held under a wire 
pointing N and S 
is deflected east 
Avhen the current is 
flowing, the direc- 
tion of the current 
is from N to S. 
Obviously, when 
the needle is held 
above the wire in 
Fig. 134, the N-pole 



will point west, since the direction of the circular field above 
the wire is opposite to its direction underneath the wire (B, 
Fig. 135). Now consider the battery terminals reversed in 
Fig. 134, so that the current flows from S to N (left to right) ; 
the direction of the circular field is reversed and the N-pole 
of the needle points west. 

When a current flows from South to North Over a needle, 
the N-end is deflected West. (C of Fig. 135.) This com- 
bination forms the word SNOW. The converse is also 
true : if the N-pole of a needle held under a wire point- 
ing N and S is deflected west, the direction of the cur- 
rent is from S to N. With the current from S to N, when 
the needle is held above the wire, the N-pole is deflected 
east (D of Fig. 135). When a current flows from N to 
S over a wire in the magnetic meridian and from S to N 
under it, the N-end of the needle is deflected east to an 
increased extent. (Compare A and D with E of Fig. 135. ) 
This forms a single turn, or convolution, and increasing 
the number of convolutions increases the extent of the 
needle's deflection till it assumes a position at right angles to 
the wire when the current is sufficiently strong. With the 



ELECTR OMA GNETISM. 



159 



current reversed in the above condition, the N-end of the 
needle is deflected west. (Compare B and C with F, Fig. 135. ) 
The current flowing in opposite directions, above and below the 
needle, increases the amount of deflection. Equal currents 
flowing above and below the needle, in the same direction, 
produce no deflection. (G, Fig. 135.) If two unequal cur- 
rents flow, one above and the other below the needle, the 
needle obeys the directive force of the stronger current. 

Exp. 51 : A simple form of apparatus for 
studying the relation between a needle' 
deflection and the direction of current 
called an Oersted stand, is shown in Fig. 
137. It consists of two parallel brass rods 
provided with binding posts and supported 
from a wooden base. With it the student 
should verify all the cases given in Fig. 
135 and make notebook sketches. 




Fig. 137.— Oersted Stand 
for Studying the Nee- 
dle's Deflections 
by a Current. 



169. Right-Hand Rule for Direc- 
tion of Whirls. — If the Direction 
of Current in any Circuit is Known, 
the Direction of the Circular Magnetic Field Around the 
Wire May be Found as Follows: 

Place the palm of the outstretched right hand above the wire, 
with the fingers pointing in the direction of the current, and the 

outstretched thumb ex- 
tended at right angles 
and underneath 
the wire. (See right 
hand, Fig. 134.) 
The direction in 
ivhich the thumb 
points will indicate 
the direction of the 
circular field around 
the wire. 





Fig. 138.— Right-Hand Rule for Finding Direc- 
tion of Current or Needle's Deflection. 



THE N 



170. Right-Hand 
Rule for Direction 
of Current or De- 
flection of Needle. 

POLE OF A NEEDLE WILL BE 



To FIND THE DIRECTION 
DEFLECTED BY A CURRENT : 

Arrange the wire above and parallel to the needle when it is at 



160 



PRACTICAL ELECTRICITY. 






rest, and place the palm of the outstretched right hand on the wire, 
with the fingers pointing in the direction of the current, Fig. 138, 
the outstretched thumb at right angles to the hand will point in the 
direction that the N-pole of the needle will turn. 

To Find the Direction of the Current when the Direc- 
tion of Deflection of the N-Pole of the Needle is Known : 

Arrange the wire N and S over the needle, and place the palm 
of the right hand over the wire, with the outstretched thumb at 
right angles to the wire and pointing in the direction that the 
N-pole turns. The fingers point in the direction that the current 
flows. This rule also holds good if the compass is above 
the wire and the right hand below it, Fig. 138. 

171. Magnetic Field of a Circular Wire Carrying a 
Current. — 

Exp. 52 : Arrange a circular turn of wire vertically and in the mag- 
netic meridian so that one-half of the circle will be above a horizontal 

piece of cardboard, as in Fig. 
139. Pass a current through 
the wire, and while tapping 
the cardboard sift iron filings 
over it. 

The iron filings arrange 
themselves circularly 
around the wire. Near 
the centre of the loop the 
filings are nearly parallel 
with its axis. Explore 
the field inside and out 

Made with the aid of iron filings. w j t J 1 a com paSS needle J 

the needle at any point lies in the direction of the filings at 
this point, and its N-pole points in the direction of the cur- 
rent's field. The arrows in Fig. 139 indicate the direction of 
the whirls, and the several positions of the needle. 

Apply the right-hand test, ^[ 170, and it will confirm the 
position the needles take up at any point. On one side of the 
loop all the whirls enter it in the same direction, and emerge 
from the opposite side as is further shown in Fig. 140. 

172. Magnetic Field at the Centre of a Circular Cur- 
rent. — If a magnetic body, A, Fig. 140, be held above the 
circular loop, through which a current is flowing, it will tend 
to move downward through the loop, with its axis coinciding 
with the axis of the loop, until its position accommodates 








139.— Graphical Field of 
Current. 



Circular 



ELECTR OMA GNETISM. 



161 




Fig. 140.— Attraction of Magnetic Body (A) by the 
Magnetic Field of the Circular Current. 



through itself the greatest number of lines of force of the cur- 
rent' s field, ^[ 43. There will be the same tendency in B, Fig. 
141, where the current is flowing in a rectangular circuit ; 
but it will be seen from 
inspection of the two 
figures that many 
more of the current's 
lines act upon the 
magnetic body, A, 
when the circuit is in 
the form of a circular 
loop than when in a 
rectangular or any 
other form, Fig. 141. 
If the distance between 
the two parallel wires 
in the rectangular circuit is equal to the diameter of the cir- 
cular loop, Fig. 140, it can be mathematically and experi- 
mentally proved that the strength of the magnetic field, at 
the centre of the circular current, is 1.57 greater than the 
strength of field midway between the two straight currents. 
For this reason nearly all magnet windings, bobbins of gal- 
vanometers, etc., are made circular to obtain the maximum 
magnetic effect of the current. 

173. Magnetic Polarity of a Circular Current. — Under 
the subject of magnetism, we assumed the magnetic lines of 
force to pass out from the N-pole of a bar magnet and enter 
the magnet again at its S-pole ; a similar reasoning is applied 
to the magnetic lines of force of an electric circuit. In the 

single turn of the cop- 
per ribbon, A, Fig. 
142, the current flows 
around the loop in the 
direction of the hands 
of a watch as viewed 
from the nearer end. 
The circular whirls are 
also clockwise, if you 
look along the ribbon 
in the direction of the current. The magnetic whirls, there- 
fore, all enter the loop through its nearer side, or face ; con- 
sequently, this face possesses S-polarity, and as the same 




Fig. 141.— Attraction of Magnetic Body (B) by the 
Current's Field. 



162 



PRACTICAL ELECTRICITY. 



AC. 




»t Clocltvvite 
Soutt. Po2d»ity 



Fig. 142.— Polarity of a Single Turn of Wire. 



lines emanate again from the more distant face, that face is 
of N -polarity. The single turn of wire, therefore, possesses 
polarity similar to a bar magnet, and when free to move will 

take up a position in 
the earth's field, with 
its N-face pointing 
toward the N ; also, 
its N-face will be re- 
pelled by the N-pole 
of a bar magnet, or 
similar loop, and at- 
tracted by the magnet's 
S-pole, according to 
the law of attraction 
and repulsion between 
magnets. When the current is sent the opposite way around 
the single turn, B, Fig. 142, the direction of the whirls is re- 
versed and the lines now emanate from the nearer or N-face 
of the loop, and enter by the more distant S-face. The po- 
larity of the loop is, therefore, reversed as compared with the 
previous case. The above 
principles may be demon- 
strated by Exp. 53. /'/ 

Exp. 53 : Fasten a piece of 
copper and zinc to a large cork, s* 
Connect the plates by a circular i\ 
turn of heavy wire, Fig. 143, V 
and immerse them in a jar con- 
taining dilute sulphuric acid. 
Present a bar magnet's S-pole 
to the N-face of the turn in the 
direction of its axis ; the coil 
will be attracted, and carrying 
the cell with it, move along the 
magnet till it reaches the mid- 
dle point, or equator. The 
figure also illustrates the direc- 
tion of the current's and mag- 
net's magnetic lines. The laws 
of attraction and repulsion 
should be verified and sketches 
made. 

174. The Helix and Solenoid. — A coil of wire wound so 
as to follow the outlines of a screw without overlaying itself 
is termed a helix. Fig. 144, and may be wound right or left- 







Fi£ 



143.— Testing the Polarity 
Single Turn of Wire. 



of a 



The turn is connected to a floating battery 
and is free to move. 



ELECTR OMA GNETISM. 



163 




Fig. 144. 



handed. The polarity can be reversed by re-winding in the 
opposite direction and passing the current, as indicated in 
Fig. 144, or by simply sending the current through the helix 
in the opposite direction. 
A solenoid is a coil of wire, 
generally wound on a 
wooden or brass spool, the 
length of which is much 
greater than the diameter, 
Fig 145. The winding is 
always in the same direc- 
tion, layer upon layer, simi- 
lar to the winding of a spool of thread. The spirals of a 
helix or solenoid are equivalent in their magnetic action to as 
many circular currents as there are convolutions of wire, since 
their axes lie in the same straight line. The magnetic whirls 
of each turn inside the helix are in the same direction as every 
other turn, and the direction of the magnetic field along, and 
parallel to the axis of the solenoid, is straight and fairly uni- 
form to within a short distance of the ends. The total field 
is the sum of the magnetic lines of each individual turn as 
illustrated in the helix, Fig. 146, where the whirls of one con- 
volution are depicted as joining on to the next, the sum of all 



-Direction of the Field of a 
Helix. 





Fig. 145. 
Solenoid. 



Fig. 146.— Polarity of the Helix. 
The whirls of one turn unite with those of the next. 



the turns constituting the field, or total number of lines of 
force passing through the helix. This diagram shows the di- 
rection of current through the helix, the direction of the 



164 



PRACTICAL ELECTRICITY. 




T+od 


J [TUj] Cork Flout 


- --_- z -. z Zn> 

7 _~_ .Sulphuric 

- ^_--_ ~_-and — ~ 


tJInlUU AcidrZ _ — _ ~~ 



Fig. 147.— Testing the Polarity of a 
Helix. 

The helix is connected to a floating cell. 



whirls around each convolution, and the resulting polarity. 
The action is similar for another set of convolutions wound 
over this set in the same direction, or for a solenoid composed 

of any number of layers of 
winding, the field increasing 
with the number of turns 
and layers so wound. 

175. Testing the Polarity of 
a Solenoid. — When a current 
is passed through a solenoid it 
is termed an electromagnetic 
solenoid, and in itsactionit be- 
haves similar to a magnet. It 
may be tested by the floating 
cell arrangement, Fig. 147, 
which is similar to that de- 
scribed in Exp. 53, or by the 
poised solenoid, Fig. 148, in 
which the two terminals of the 
movable solenoid dip into two 
concentric circular grooves con- 
taining mercury in which con- 
tact is made. One groove is connected to each binding post by a wire, 
the groove stain ped A, corresponding with post A, so that the direction 
of the current may be traced. When a current is sent through the 
coil it takes up a position N and S just as in the case of the poised 
needle, and is also repelled or 
attracted by another magnet 
or solenoid, the polarity being 
as explained for a single con- 
volution, T[ 172. 

176. Rules for Deter- 
mining Polarity of a Sole- 
noid. — Clasp the solenoid, 
or helix, in the right hand 
so that the fingers point 
around it in the direction 
that the current flows. The 
outstretched t h u m b, at 
right angles with the fin- 
gers, will point in the di- 
rection of the N-pole of the 
solenoid, Fig. 149. 

To find the direction of current around the coil when the 
polarity is known : clasp the coil with the right hand, so that 




Fig. 148.— Ampere Frame Stand with 

Coils. 
The movable coils are poised on needle points 
and the terminals dip in concentric 
mercury caps. 



ELECTRO MA GNETISM. 



165 



the thumb outstretched at right angles will point toward the 
N-pole, then the fingers will point in the direction of the cur- 
rent. 

If on viewing the 
end of a solenoid the 
current flows around 
that end, in the same 
direction that the 
hands of a watch 
move, Fig 150, that 
end is S-polarity. If 
the c u r r e n t flows 
around the coil against 
the direction in which 
the hands of a watch move, that end possesses N -polarity. 

177. Graphical Field of a Solenoid.— The distribution 
of magnetism around a solenoid is very similar to that of a 
bar magnet, and can be studied 
by the iron filing diagram, Fig. 
151. 



DIRECTION OF 
MAGNETIC FORCE 



Fig. 149. 




-Right-Hand Rule for the Polarity 
of a Solenoid. 



Exp. 54 : Cut a piece of cardboard 
to fit around a solenoid, as in Fig. 151. 
Place the cardboard horizontally so 
that its plane is in the axis of the coil. 
Pass a current through the coil, and 
while gently tapping the cardboard 
sift iron filings on it to produce a 
graphical field. 





w\ 



Ay .f» 



.'",'/ 
















Fig. 150.— Clock Rules for Polarity 



Fig. 151.— Magnetic Field of a 
Solenoid. 

Made by iron filings upon a horizontal 
piece of cardboard. 



Exp. 55 : Wind a helix about 1 inch in diameter and 4 inches long. 
Cut a tongue in a sheet of cardboard equal to the inside diameter of 
the helix, and pass it horizontally through the helix with its plane 
in the axis of the helix. Make a graphical internal field of the helix. 
The direction of the lines of force may also be explored by a com- 
pass needle. 



166 PRACTICAL ELECTRICITY. 

QUESTIONS. 

1. A feed wire for the overhead trolley line is conducted up 
a vertical wooden pole from an underground duct. When you 
approach the pole from the S the N-end of a compass needle held in 
your hand is deflected east. Is the current flowing up or down 
the pole? 

2. One end of an arc lamp solenoid attracts the N-pole of a com- 
pass needle. What is the direction of the current around the coil 
when viewed from this end ? 

3. There is a leak to ground on a telegraph line between two sta- 
tions 50 miles apart, so that the current transmitted does not reach the 
receiving apparatus. State how, by the use of a compass needle, you 
would proceed to accurately locate the point at which the leak exists ? 
Make sketch. 

4. Two parallel lines, one above the other, are stretched in a N and 
S-direction, and an equal current flows through each in the same 
direction. A compass is held midway between the wires. How will its 
needle be affected ? Make sketch. 

5. Six successive turns are made in a right-hand direction around 
a lead pencil, and the following six successive turns are wound in the 
opposite direction. A current is passed through the wire. Sketch 
the direction of the magnetic field you would expect to see if iron 
filings were used, and indicate the polarity and direction of the cur- 
rent. 

6. A current is sent through a coil of wire wrapped around a 
tumbler in the same direction that the fingers of the right hand point 
when clasping it to drink. What is the polarity of that end of the coil 
you observe while drinking ? 

7. A current is passed through a wire held east and west over a 
compass needle. How will the needle be affected? Make sketch. 

8. You are given the terminals of a cable containing the positive 
and negative poles of 5 batteries. The terminals are to be connected 
so that the cells will all be in series. How would you proceed by the 
use of a galvanometer to determine the polarity and make the con- 
nections? Give sketch. 

9. The N-pole of a bar magnet, lying on a table with its axis point- 
ing east and west deflects the N-pole of a compass needle 20 degrees. 
A wire carrying a current is held over the compass in a N and S- 
direction and the deflection is now only 12 degrees. How do you 
account for this ? 

10. What is the direction of current through the wire in question 9 ? 
Make sketch. 

11. An electric light wire is run up the S-wall of a building from 
the first to the second story. Walking toward the wire the N-pole of 
a compass held in your hand is deflected east. What is the direc- 
tion of the current in the wire? Make sketch. 

12. There is a break in a 5-pound spool of magnet wire. How 
would you proceed to locate it by the use of a battery and galva- 
nometer ? 



LESSON XVI. 



GALVANOMETERS. 

Principle of the Galvanometer — Detector Galvanometer — The Use of 
Long and Short Coil Galvanometers — Classification of Galvanom- 
eters — Relative Calibration of a Galvanometer— Tangent Galva- 
nometer — Table XI. Natural Sines and Tangents — The Tangent 
of an Angle — Student's Combination Tangent Galvanometer — 
Directions for Setting up Student's Combination Galvanometer — 
Variation of Needle's Deflection with the Turns and Diameter of 
the Galvanometer Coil — Use of the Tangent Galvanometer as an 
Ammeter — Table XII. Tangent Galvanometer Constants — 
Thomson Mirror Reflecting Galvanometer — Astatic Differential 
and Ballistic Galvanometers — D' Arson val Galvanometer — Ques- 
tions. 

178. Principle of the Galvanometer. — An instrument 
which measures a current by its electromagnetic effect is called 
a galvanometer. Galvanometers are used for detecting the 
presence of an electric current 
in any circuit,- and for deter- 
mining its direction, strength 
and pressure. Their construc- 
tion is based on the principle 
that a magnetic needle, or its 
equivalent, is deflected when 
brought under the influence of 
a magnetic field, such as that 
of a wire through which a cur- 
rent is flowing. A simple gal- 
vanometer consists essentially 
of a magnetic needle poised 
or suspended in the centre of a 
coil of wire, and provided w T ith 
a circular scale, graduated in 
degrees, on which the devia- 
tion, or deflection, of the needle 
may be noted. When such an instrument is connected in a 
circuit the presence of the current is shown by the deflection 
of the needle. The direction of the current is shown by the 

167 




Fig. 152.— Simple Galvanometer. 



168 



PRACTICAL ELECTRICITY. 




Fig. 153.— Student's Detector 
Galvanometer. 



side towards which the N-pole of the needle moves, ^[ 168. 
The strength of current is indicated by the amount of the 
needle' s deflection ; since the position the needle takes up 
depends upon the relative magnitude of the magnetic forces, 

due to the current and the earth. 
The earth's magnetism may be con- 
sidered to be approximately constant 
at any particular place. 

To obtain the maximum effect of 
the current's field, the galvanometer 
wire or coil, when no current is flow- 
ing, is arranged parallel to the mag- 
netic needle when it is at rest, 
so that the plane of the coil passes 
through the axis of the needle and 
the magnetic meridian. Galvanom- 
eters are usually set up to conform to the above conditions before 
sending a current through them; the current's field will then 
act at right angles to the earth's field, and the position the 
needle will take up when the current flows is the resultant of 
these two forces. A certain amount of the current's field is 
therefore used to 
overcome the earth's 
attraction for the 
needle before it 
moves at all. When 
the needle is deflect- 
ed to 90 degrees, 
or at right angles 
to the wire, it is in 
the maximum 
position of the cur- 
rent's field. The 
value of the deflec- 
tion is dependent 
upon the current 
flowing through the 
coil, but is not pro- 
portional to the current ; that is, if one current produces twice 
the number of deflections of another current the former is not 
of twice the strength, ^[ 182. With the needle parallel to 
the coil, or at the zero scale position, a small current deflects 







s^ .Oj~. ^ c. . - • /Ste 



S&t&S, 



ue*W&«f»<r< 






Fig. 154. 



-Construction of Student's Detector 
Galvanometer. 



GAL VANOMETERS. 1 69 

it considerably, but as the angle the needle makes with the 
coil increases, a much greater magnetic force is required. 
For example, it requires a greater force to deflect the needle 
one degree from the 45-degree position than to deflect it one 
degree from the 1 5-degree position. The galvanometer coil 
may be wound with a great many turns of fine wire, in which 
case the instrument is said to be sensitive ; that is, the needle 
is appreciably deflected by a very small current ; or it may be 
composed of a few turns of very heavy wire, in which case it 
is intended for use with large currents. 

By the sensibility of a galvanometer is meant the amount of 
current required to produce a given deflection. The sensi- 
bility is sometimes rated in ohms. For example, a galvanom- 
eter with a sensibility of 2 megohms, *\\ 126, means that if 
it is connected in series with 2 megohms and a potential of 
1 volt applied to the circuit, the movable system will be de- 
flected one division of the scale. The sensibility of a galvanom- 
eter, therefore, depends upon the number of times the cur- 
rent circulates around the coil, the distance of the needle 
from the coil, the weight of the needle, and the amount of 
friction produced by its movement. The needle is usually 
quite small, and often a compound one. See ^| 187. In very 
sensitive galvanometers the coils are wound with thousands 
of turns of very fine wire, and shunts are generally used in 
connection with them. 

179. Detector Galvanometer. — 

A student's detector galvanometer is illustrated in Fig. 153, and the 
sectional parts in Fig. 154. A circular glass-covered box contains the 
magnetic system inclosed in a rectangular coil of finely wound wire. 
An aluminum pointer is fixed to an aluminum cap, Fig. 154, and the 
magnetic needle fastened to a glass jewel. The cap telescopes the 
jewel and the pointer is arranged at right angles to the needle. One- 
half of the dial is graduated in degrees and the other half in divi- 
sions corresponding to the tangents of the various angles, fi 184. In 
adjusting this instrument for use, turn the box around till the pointer 
is directly over the zero mark on the scale ; the pointer will then 
point east and west, and the magnetic needle at right angles to it will 
be in the magnetic meridian, as will also the coil of wire. The coil is 
wound with No. 30 B. & S. magnet wire, and has a resistance of about 
30 ohms. The instrument is very sensitive ; a current of about .00001 
ampere will deflect the needle 1 degree. 

180. The Use of Long and Short Coil Galvanometers. 

In making electrical measurements it is necessary to use 
current. Suppose it is desired to measure the resistance of 



170 



PRACTICAL ELECTRICITY. 



the cotton insulation around a piece of wire, Fig. 155 ; a cur- 
rent must be passed from the sheet of tin foil wrapped around 
the insulated wire, through the cotton insulation to the wire 
itself. The value of this current is to be noted on the gal- 
vanometer. The current will be very small that flows 
through, say one-eighth inch of cotton, so that the galvanome- 
ter must be extremely sensitive to record such a minute cur- 
rent, therefore the coil should be small in diameter and wound 
with many turns of very fine wire, and the needle arranged 
to eliminate as much friction as possible. On the other hand, 
suppose it is desired to indicate the current flowing through 
a number of incandescent lamps if a fine wire or long coil 
galvanometer is connected in series with the lamps; either the 
resistance would be so high that the lamps would not light, 
or the coil would be heated and destroyed, due to an exces- 
sive current passing through it, % 257. 
A short thick coil galvanometer of a 
large diameter, containing one or more 
turns, and consequently very low re- 
sistance, is suitable for this case. The 
total magnetising force deflecting the 
needle may be the same as before, but 
produced by a large current circulating 
around a few turns instead, of a small 
current, around thousands of turns, 
IT 197. 

Long coil galvanometers of very 
high resistance are used to measure 
electrical pressure, and when properly 
standardized their scales are graduated 
directly in volts and the instrument 
then becomes a voltmeter, % 233. The 
standardization consists in experimentally determining the 
position of the needle, when the coil is subjected to different 
known pressures, and marking these values on the scale ; the 
process is called calibration and the galvanometer is calibrated 
absolutely as a direct reading instrument. It is still the cur- 
rent that deflects the needle, and its strength is dependent 
upon the pressure. Short coil galvanometers of very low 
resistance have their scales calibrated to read directly in 
amperes, and thus become amperemeters or ammeters, ^f 203. 
181. Classification of Galvanometers. — According to the 




Fig. 155. — Measuring In- 
sulation Resistance. 



GALVANOMETERS. 171 

principle of action, galvanometers may be divided into two 
classes ; first, those in which the magnet or magnetised body 
is arranged to move and the coil held stationary, and second, 
those in which the magnet is stationary and the coil arranged 
to move. Each class is largely used in practice for laboratory 
and commercial purposes, and constructed in a variety of 
forms. In construction, the winding used may be ' ' long coil ' ' 
or ' ' short coil] ' and the method of supporting the magnetic 
system either by suspension, by poising it, or by delicate 
springs. The deflections may be noted either by a pointer 
attached to the magnetic system and moving over a graduated 
scale, or by a small mirror attached to the system. A ray of 
light focused upon the mirror is reflected upon a scale at 
some distance and greatty enlarges a small movement of the 
magnetic system. In another method the image of the scale 
deflection is observed on the mirror by a telescope located at 
about the same distance as the scale, % 189. Long coil gal- 
vanometers may be used as short coil galvanometers when a 
shunt is employed, *\\ 162. 

182. Relative Calibration of a Galvanomter. — 

Exp. 56 : Shunt the detector galvanometer, f 162, with about 4 
feet of No. 18 magnet wire and connect the shunted instrument in 
series with the gas voltameter, f 120, and a source of E. M. F. Allow 
the current to pass for about five minutes and note the average deflec- 
tion of the needle. (Find the average deflection by dividing the sum 
of all the readings, taken at one-half minute intervals, by the num- 
ber of readings so taken.) Calculate the current by Formula (7), 
corresponding to the average deflection it produced, and place results 
in table for comparison. Repeat a number of such tests and calcula- 
tions, using each time a different E. M. F. In such a test the follow- 
ing results were obtained from the calculations for a particular 
shunted galvanometer : 

Degrees. Amperes. 

25 0.5 

35 0.75 

40 1.0 

45 1.05 

The above shunted galvanometer is said to be calibrated 
relatively. Suppose that when it is used in another circuit 
with the same shunt, the deflection produced by an unknown 
current is 30 degrees, then by reference to the table the ap- 
proximate current will be .62 ampere, since .5 ampere pro- 
duces 25 deflections and .75 ampere, 35 deflections. That the 
deflections are not proportional to the current is also shown 



172 PRACTICAL ELECTRICITY. 

by this test, If a new scale were made for the instrument 
and .5 ampere substituted for the 25 degree mark and so on, 
then we would have an absolute calibration of the instrument, 
or practically, a shunted ammeter, ^[ 209. 

Exp. 57 : Connect a rheostat of several hundred ohms in series 
with the detector galvanometer, ^ 179, to one Daniell cell, assumed 
to give 1 volt E. M. F., and record the deflection corresponding to this 
pressure. Make a number of tests, using each time a different num- 
ber of cells connected in series, and tabulate results as below : 



Deflections. 


Volt; 


17 


1 


30 


2 


40 


3 


45 


4 



The galvanometer is now relatively calibrated as a voltmeter. Suppose 
a dry cell, when connected to the galvanometer and extra resistance 
in series, gives 21 deflections ; then its E. M. F. is between 1 and 2 
volts, approximately 1.4 volts by proportionate calculation from the 
test. The calibration could be made absolute, as in Exp. 56. 

183. Tangent Galvanometer. — The tangent galvanome- 
ter is so called because a particular function of each angle of 
the needle's deflection, called a tangent, is directly propor- 
tional to the current flowing through the instrument. There 
is, therefore, a direct law between the current and deflections 
when the instrument is properly constructed. The magnetic 
needle, which should be very small as compared with the 
diameter of the coil (for example, needle .75 inch, diameter 
of coil 8 inches), is poised or suspended in the centre of a 
coil of large diameter, of one or more turns, Fig. 158. In 
|F - the centre of such a coil the magnetic field 
i is practically uniform, Fig. 139. The axis 
{o of the needle is parallel to the coil when no 
i current is flowing, both being, therefore, 
in the magnetic meridian. 

,]c 184. The Tangent of an Angle.— 

Instead of measuring an angle in degrees of an 
-Aurc, it may be reckoned by some function of the 
angle. In Fig. 157 the position of the galvanom- 
eter needle when pointing to zero on the circular 
scale is represented by the line AB. Draw an 

■& -ic^ tuTI t> indefinite line, AF, perpendicular to AB, and 
x iff. 15/. — Ine lan- A . , ., ' . . ; r ^ r . * n it- 

gent of an Angle, tangent to the circle at point A. buppose the 
needle is now deflected by the current to a point 
along the line BC, making the angle ABC of a certain number of 
degrees. The line, AC, is called the tangent of the angle ABC. The 




GALVANOMETERS. 



173 



value of the tangent of an angle (length of line AC) increases as the 
angle opens out or increases ; thus, if another current deflects the 
needle along the line BD, making the angle ABD of so many more 
degrees, the tangent of this angle is represented in value by the 
length of the line AD. When the needle is deflected at right angles, 
or 90 degrees, the radius prolonged will not intersect the tangent line, 
or, the tangent of 90 degrees is infinity. The values of the tangents 
vary from to infinity. If the value of the radius be unity, or one, 
the tangent of 45 degrees will be equal to one (that is, the length of 
line AB = AC), so that the value of the tangent of any angle less 
than 45 degrees will be less than one, and of a larger angle than 45 
degrees more than one. The value of the tangents for each angle is 
given in the following table. For example, the tangent of 70 degrees 
is 2.7475, which means that if the length of radius AB is 1, the length 
of the line AC is 2.7475 times as great as the radius. 









Table XI.— Natural Sines and Tangents 








1 


Sin. 


Tan. 


l 


Sin. 


Tan. 


Z 


Sin. 


Tan. 


I 


Sin. 


Tan. 


Z 


Sin. 


Tan. 


0° 


.0000 


.0000 


18° 


.3090 


.3249 


36° 


.5878 


.7265 


54° 


.8090 


1.3764 


72° 


.9511 


3.0777 








19 


.3256 


.3443 








55 


.8192 


1.4281 


73 


.9563 


3.2709 


1 


.0175 


.0175 








37 


.6018 


.7536 


56 


.8290 


1.4826 








2 


.0349 


.0349 


20 


.3420 


.3640 


38 


.6157 


.7813 








74 


.9613 


3.4874 


3 


.0523 


.0524 








39 


.6293 


.8098 


57 


.8387 


1.5399 


75 


.9659 


3.7321 








21 


.3584 


.3839 








58 


.8480 


1.6003 


76 


.9703 


4.0108 


4 


.0698 


.0699 


22 


.3746 


.4040 


40 


.6428 


.8391 


59 


.8572 


1.6643 








5 


.0871 


.0875 


23 


.3907 


.4245 














77 


.9744 


4.3315 


6 


.1045 


.1051 








41 


.6561 


.8693 


60 


.8660 


1.7321 


78 


.9781 


4.7046 








24 


.4067 


.4452 


42 


.6691 


.9004 








79 


.9816 


5.1446 


7 


.1219 


.1228 


25 


.4226 


.4663 


43 


.6820 


.9325 


61 


.8746 


1.8040 








8 


.1392 


.1405 


26 


.4384 


.4877 








62 


.S829 


1.8807 


80 


.9848 


5.6713 


9 


.1564 


.1564 








44 


.6947 


.9657 


63 


.8910 


1.9626 














27 


.4540 


.5095 


45 


.7071 


1.0000 








81 


.9877 


6.3138 


10 


.1736 


.1763 


28 


.4695 


.5317 


46 


.7193 


1.0355 


64 


.8988 


2.0503 


82 


.99«3 


7.1154 








29 


.4848 


.5543 








65 


.9063 


2.1445 


83 


.9925 


8.1443 


11 


.1908 


.1944 








47 


.7314 


1.0724 


66 


.9135 


2.2460 








12 


.2079 


.2126 


30 


.5000 


.5774 


48 


.7431 


1.1106 








84 


.9945 


9.5144 


13 


.2250 


.2309 








49 


.7547 


1.1504 


67 


.9205 


2.3559 


85 


.9962 


11.43 








31 


.5150 


.6009 








68 


.9272 


2.4751 


86 


.9976 


14.30 


14 


.2419 


.2493 


32 


.5299 


.6249 


50 


.7660 


1.1918 


69 


.9339 


2 6051 








15 


.2588 


.2679 


33 


.5446 


.6494 














87 


.9986 


19.08 


16 


.2756 


.2867 








51 


.7771 


1.2349 


70 


.9397 


2.7475 


88 


.9994 


28.64 








34 


.5592 


.6745 


52 


.7880 


1.2799 








89 


.9998 


57.29 


17 


.2924 


.3057 


35 


.5736 


.7002 


53 


.7986 


1.3270 


71 


.9455 


2.9042 









When it is desired to compare the relative strength of two currents, 

each is passed through the tangent galvanometer, properly set up, and 

the corresponding deflections noted. The first current will bear the 

same relation to the second current that the tangent of the first angle 

bears to the second angle. The value of the tangents is taken from 

the table. Calling C and C { the two currents to be compared and d 

and d r the deflections produced by these currents respectively, then : 

C is to C x as tan of d is to tan of d 1} 

C tan d /_, v 

or FT = - T , (51). 

Ci tan d x v ' 

p C! X tan d 



Or 



tan d x 



174 



PRACTICAL ELECTRICITY. 



Prob. 66 : A tangent galvanometer is deflected 17° when inserted in 
series with a solenoid and a Daniell cell. When a Grenet cell is 
substituted the deflection is 31°. What is the relative strength of 
current through the solenoid when the Grenet cell is used ? 



By Formula (51) C = 



CjXtand _C 1 X.3 



or C = -a C x , .or 



as the current from the 



.6. 



tan dj .6 

the Grenet cell current was twice as strong 
Daniell cell. 

d = 17°, tan d = .3, d x = 31°, tan d x 

Prob. 67 : If one ampere deflects the needle of a tangent galvanom- 
eter 5° how many amperes will deflect it 50° ? 

t? ^ i ,ki\ n Cxtandi ' 1 X 1.1918 

From Formula (51) C x = — t d — = — Qgyr = 13.6 amperes. 

C= 1 ampere, d = 5°, tan d = .0875, d! = 50°, tan d x = 1.1918. 
If a tangent galvanometer is constructed or adjusted so that one 
ampere deflects the needle 45°, since the 
tangent of 45° equals one, the value of any 
other angle of deflection will represent the 
value of the current in amperes passing 
through the instrument. 

185. Student's Combination Tan- 
gent Galvanometer. — 

For many laboratory measurements the 
combination tangent galvanometer, illus- 
trated in Fig. 158, may be used. It consists 
of the detector galvanometer (described in 
H" 179) placed in position in the tangent coil 
frame, 8 inches in diameter, constructed of 
hard wood and mounted on a suitable base. 
The detector galvanometer is readily re- 
moved from the frame so that it may be 
used separately when desired. When placed 

in position its needle is in the centre of the coils on the frame and the 

current is passed through the outer coils 

only. There are four coils of No. 18 wire 

wound on the frame with two turns per 

coil. The terminals of each coil are con- 
nected to binding posts ; the figure shows 

the binding posts of two coils, the other 

four posts being on the opposite side. 

Three brass leveling screws underneath 

the base are used to level the instrument 

so that the glass jewel rides freely on its 

pivot. 

Fig. 159 shows a diagram of the method 

of winding. The coils are all wound in 




Fig. 158.— Student's Tan- 
gent Galvanometer. 




the same direction, B representing the Fig> 159 —Method of Wind 



beginning of a coil and E its ending. The 
advantage of the separate coils is that they 



Coils in Student's Tan- 
gent Galvanometer. 



rig 



GALVANOMETERS. 



175 



maybe connected up in a number of different ways to illustrate the 
law of series and parallel circuits, and the magnetic effect upon the 
needle by varying the number of turns around it. Figs. 160 A, B and 
C, illustrate several connections of the galvanometer coils, and the 
turns, or number of times the total current would flow around the 
needle are also given in each case. 

186. Directions for Setting up Student's Combina- 
tion Galvanometer. — 

Seat the detector galvanometer on the horizontal support of the 
coil frame, Fig. 158, by means of the projecting wooden pin. Turn 
the frame so that it points N and S, with its plane in the magnetic 
meridian. You cannot see the magnetic needle directly underneath 
and parallel to the frame when it is at rest, and for this reason the 
pointer is fixed at right angles to it. Now revolve the detector gal- 




A All Co.i 



i Series -STurna B. Two Coils in SeriM witfc 
T«voinPor<ai«)-6Turn» 



Parol Id 



Fig. 160. — Connections of Coils in Student's Tangent Galvanometer. 

vanometer on its wooden pivot so that the zero position on the 
scale lies directly underneath the pointer. Send a current through 
the four coils in series, and the deflection is, say 44° to the right ; 
reverse the current, and if the deflection is 44° to the left, the 
needle and coil are in the magnetic meridian. If the latter de- 
flection had been 48° then the coil frame must be moved a little 
in the opposite direction to that of the greater deflection, and 
zero position again adjusted to the pointer with no current flowing. 
This adjustment should be made until the needle deflects equally 
on both sides of the zero mark for the same strength of current. 
Deflections may be read from the degree scale of the instrument and 
the tangents obtained from the table, or the deflections on the tan- 
gent scale are directly proportional to the current. The resistance of 
the four coils connected in series is .165 ohm, and a current of 0.25 
ampere sent through them will deflect the needle 45°. 

187. Variation of Needle's Deflections with the Turns 
and Diameter of the Galvanometer Coil. — 

Exp. 58 : Send a current of known strength, say .5 ampere, around 
one coil of the galvanometer, ^ 185, and note the deflection on the 
tangent scale. The current flows twice around the needle, since 
there are two turns per coil. Pass the same strength of current 
through two coils in series. The current flows four times around the 



176 PRACTICAL ELECTRICITY. 

needle and it is deflected to a value on the tangent scale double that of 
the first case. If three coils are used in series the tangent scale value 
is tripled. Note also the degree scale deflections, and compare the 
value of the tangents taken from the table for each deflection. 

The sensibility, ^| 178, of the galvanometer is therefore 
directly proportional to the number of convolutions of wire 
on the coil. If the coil had been increased to twice the 
diameter and the same strength of current passed twice 
around it, the tangent of the angle of deflection would have 
been just one-half that produced by the same current flow- 
ing twice around the smaller coil ; therefore, the sensibility is 
also inversely proportional to the diameter of the coil, de- 
creasing the diameter, increasing the sensibility, and vice 
versa. 

188. Use of the Tangent Galvanometer as an Ammeter. 

The value of any current sent through the tangent galvanometer may 
be calculated directly in amperes from the following formula, when the 
dimensions of the instrument are known. The needle is supposed to 
move in a horizontal plane and not controlled by any force but the 
earth's magnetism. 

Let C = current in amperes ; 

N = radius of coil in inches ; 
r = number of turns in coil ; 

d = angle of deflection of needle ; 

H = a constant from the table below. 

Then, C = -*- r X tan d , (52). 

The constant, H, given in the following table represents the hori- 
zontal force of the earth's magnetism for the place where the galva- 
nometer is used. It may be approximated for other localities not in- 
dicated. The values given were furnished t>y the IT. S. Geodetic Bu- 
reau for the epoch 1900 and are for square inch measure. Each value 

f>_ 

has been multiplied by -j-q s0 tnat Formula (52) is fcorrect as given. 

Table XII.— Tangent Galvanometer Constants.— Values of H. 

Boston .699 

Chicago .759 

Denver .919 

Jacksonville 1.094 
London .745 

Minneapolis .681 

New York .744 

Since the tangent of the angle of deflection in Formula (52) is 

H X r 

always to be multiplied by a constant number, — ^— ' for a particu- 
lar instrument and place, this value is called the constant of the galva- 
nometer. 



New Haven 


.731 


Philadelphia 


.783 


Portland, Me. 


.674 


San Francisco 


1.021 


St. Louis 


.871 


Washington 


.810 



GALVANOMETERS. 



177 



To FIND THE CURRENT IN AMPERES FLOWING THROUGH THE INSTRUMENT : 

Multiply the tangent of the angle of deflection by the galvanometer constant. 

HXr. 



Let K = constant of the galvanometer = 

C = current in amperes ; 

d = deflection of needle. 

Then, C = K X tan d 



N 



(53; 



Prob. 68 : A Daniell cell is connected to 4 coils of the student's tan- 
gent galvanometer connected in series, 1} 154, and the needle is de- 
flected 30 degrees. The diameter of the coil is 8 inches, and with 4 
coils in series with 2 turns per coil, the total turns are 8. What cur- 
rent is flowing through the instrument if it 
is located in New York ? 
By Formula (52) 



IXr Xtand=- 744X4 X 




N 



.5774 = 



.214 ampere. 

H for New York =.744, r = 4 inches 
radius, N = 8 turns, tan d= .5774. 

Prob. 69 : What is the constant of the 
galvanometer in Prob. 68 ? 

jr- HXr .744 X 4 Q79 
K=-^- = g— =.372. 

Prob. 70 : A bichromate cell is connected 
to the galvanometer referred to in Probs. 68 
and 69. What current flows through the 
instrument if the needle is deflected 50 
degrees ? 

By Formula (53) C = K X tan d = .372 X 
1.1918 = .443 ampere. 

K for the galvanometer = .372 from Prob. 
69, tan d = 1.1918. 

189. Thomson 
Galvanometer. — 

In this type of instrument, Figs. 161 and 
162, great sensibility has been attained by 
bringing the 
coil as close 
to the needle 
as possible) 
and winding 
it with many 
Fig. 161.— Thomson Mirror- turns of very 
Reflecting Galvanometer fine wire 

(single coil). 0n th eback 

of a small mirror, about i inch in diameter, are fastened by shellac, a 
number of magnetic needles with their N-poles in one direction. The 
mirror is suspended in the centre of the coil, so that the needles hang 

12 




Mirror-Reflecting 




Fig. 162.— Details of the Coil. 



178 



PRACTICAL ELECTRICITY. 



horizontally, by a fine cocoon silk fibre which extends the entire 
length of the vertical brass tube shown in Fig. 161. To facilitate the 
insertion of the magnetic system in the centre of the coil, it is wound 
in two sections, which are bolted together in the cylindrical brass 
box, leaving a small space between them through which the fibre 
suspension passes. The coil is completely enclosed from the atmos- 
phere, which assists in renderingthe instrument dead-beat in its action, 
i. e., so that the magnetic system may come to rest almost instantly 
without first making a number of vibrations when the circuit is made 
and broken through the instrument. The pent up air produces a 
cushion effect upon the vibrating mirror, causing it to come to rest 
more quickly. The cylindrical box is mounted on a tripod, provided 




Fig. 163 — Thomson Mirror-Reflecting Galvanometer with Lamp, Stand, Scale and Con- 
nections of Apparatus for Measuring the Insulation Resistance of an Electric Cable. 

with leveling screws, and can be rotated on its vertical axis. The 
curved controlling magnet, arranged on the vertical tube, can either 
be revolved, or raised and lowered, with regard to the magnetic 
needle. By turning it around the axis of the tube the mirror with 
its needle may be deflected to any position on the scale and the sen- 
sibility increased or decreased by raising or lowering the magnet, 
thereby increasing or decreasing its attraction for the needle. The 
instrument is most sensitive when placed with its coil in the magnetic 
meridian, with the controlling magnet elevated to such a position 
that its force upon the mirror's magnet just balances the action of the 
earth's attractive force upon the same. 

A mirror reflecting galvanometer with its lamp, stand and scale, 
is shown in Fig. 163, and requires a darkened room for its operation. 



GAL VANOMETERS. 



179 



A small vertical slit is cut in the lamp screen below the scale, and 
the ray from the lamp passing through this slit strikes the galvanom- 
eter mirror, which is about one yard distant. The galvanometer is 
adjusted so that the reflected beam of light strikes the scale. The 
zero position on the latter is 
located at the centre so that 
the beam swings to the right 
or left of zero, and is brought 
to zero position by the con- 
trolling magnet, or by twisting 
the fibre suspension by means 
of the knurled knob at the top 
of the tube. The angle be- 
tween the original beam of 
light and the reflected beam 
will be twice the angle of the 
deflection of the mirror ; the 
deflections of the spot of light 
on the scale, however, are 
practically proportional to the 
strength of currents through the instrument. When a telescope is 
substituted for the lamp, as in Fig. 164, a dark room is not required. 

The scale readings are reflected 
in the mirror and their value ob- 
served by means of the telescope. 

190. Astatic, Differential 
and Ballistic Galvanometers. 

If two needles of equal strength 
are fastened to a vertical rod with 
like poles in opposite directions 




Fig. 164.— D'Arsonval Mirror- Reflecting Galva- 
nometer with Scale and Reading Telescope. 





Fig. 165.— Connections of Single Coil 
Astatic Galvanometer. 



forming an astatic needle, ^ 58, and 
suspended, the earth's field has 
almost no directive force on the 
magnetic system. Since the earth's 
attraction for this needle has been 
thus neutralized, a much smaller 
current will deflect it than when 
the earth's directive force has to 
be overcome. This principle is 
used in increasing the sensibility of galvanometers. In Fig. 165, 
the galvanometer coil surrounds the lower needle and the direction 
of current between the two needles tends to turn them the same way. 
This method is used in the astatic galvanometer, Fig. 166, which is 



Fig. 166.— Single Coil Mirror-Reflecting or 
Direct Scale Astatic Galvanometer. 



180 



PRACTICAL ELECTRICITY. 




Fig. 167.— Connections of 

Double Coil Astatic 

Galvanometer. 



arranged so that the deflections may be read from the circular scale, 
or the instrument may be used as a mirror-reflecting galvanometer, by 
means of the small mirror attached to th. vertical fibre suspension. 
A controlling magnet is also provided to bring the needle system to 
zero and alter its sensibility. A coil sometimes 
surrounds each needle as shown in Fig. 167, in 
which case they are connected so that the 
direction of current in both coils will tend to 
turn the system in the same direction. 

The Thomson mirror-reflecting astatic galva- 
nometer, Fig. 168, is so constructed. The in- 
strument is illustrated with the front swung 
open so that each half of each coil, as well 
as the astatic system, may be noted. The 
needles are compound and fastened to a small mica disc and rigidly 
joined together by a fine glass rod ; midway between the needles is 
fastened the mirror, mounted on a mica vane and secured to the 

glass rod. The mica 
vane assists in damp- 
ing by fanning the air 
when the needles are 
deflected. The whole 
system is suspended 
by a cocoon fibre at- 
tached to the upper 
end of the glass rod 
andextendingthrough 
and protected by the 
vertical brass tube. 
When the door is 
closed the mirror may 
be seen through a 
glass window. Bind- 
ing posts are provided 
for the terminals of 
each coil and the coils 
may be connected in 
series, parallel, etc., 
care being exercised 
to have the direction 
of current as given in 
Fig. 167. The coils of 
each needle may be 
used separately for 
comparing two differ- 
ent current strengths 
at the same time, 
when the direction of 
the current in each is 
such as to tend to turn 
the mirror oppositely. 
When so used the instrument is called a differential galvanometer. 
In a special form of mirror reflecting galvanometer called a ballistic 




Fig. 168.— Thomson Mirror-Reflecting Double Coil 
Astatic Galvanometer with Case Open. 



GALVANOMETERS. 



181 



galvanometer, used for measuring momentary currents (as induction 
currents or the discharge of a condenser, fl 803), the magnetic system 
is constructed so as to have considerable weight, and arranged to 
give the least possible damping effect. If a momentary current be 
passed through its coils, the impulse given to the needle does not 
cause appreciable movement of the magnetic system until the current 
ceases, owing to the inertia of the heavy moving parts, the result 





Fig. 169. — D'Ai-sonval Mirror 

Reflecting Galvanometer. 

Vertical magnet form. 



Fig. 170. — D'Arsonval Mirror- 
Reflecting Galvanometer. 
Horizontal magnet form. 



being a slow swing of the needle. The maximum deflection is noted 
on the scale just at the point where the system ceases to move and 
begins to swing back to zero. 

191. D'Arsonval Galvanometer. — This galvanometer, 
illustrated in Figs. 169 and 170, is an example of that class 
in which the magnet is large and stationary, and the gal- 
vanometer coil small and free to move, when a current is sent 
through it. A coil of wire wound upon a rectangular bobbin 
is suspended by fine silver wires between the poles of a lami- 
nated horseshoe magnet, so that the horizontal axis of the coil 
is at right angles to the magnetic lines of force between the 



182 



PRACTICAL ELECTRICITY, 



poles of the magnet. When a current is led to and from the 
coil by means of the suspension wires above and below it, the 
coil becomes a magnetic body, and tends to turn so that its lines 
of force will be in the same direction as those of the perma- 
nent magnet field. This tendency to rotate is opposed by 
the torsion of the suspension wire. The coil will move to 
the right or left, depending upon the direction of current 
through it. A stationary piece of soft iron is arranged in the 
centre of the coil and supported from the back, 
its purpose being to increase the strength of 
the magnetic field in which the coil moves. By 
properly shaping the pole pieces the magnetic 
field may be so varied that the deflections will 
be directly proportional to the current. 

If the coil is wound upon a non-magnetic 
metallic frame, the instrument is very dead- 
beat, as the instant the coil moves induced cur- 
rents are set up in the coil frame, and are in 
such a direction as to tend to stop its move- 
ment, ^| 292. A mirror is attached to the coil 
so that the instrument may be used with a 
telescope and scale, Fig. 164 ; or a pointer may 
be added, fixed at right angles to the mirror 
and made to sweep over a circular scale attached 
to the magnets. Another form of D'Arsonval 
galvanometer is shown in Fig. 170, in which 
the magnets are horizontal. The coil is sus- 
pended in a brass tube containing a window, 
opposite the mirror. The tube is clamped in 
position between the specially shaped pole 
pieces and can be readily removed and replaced 
by another of higher or lower resistance, as de- 
sired. Details of the tube and its casing are 
shown in Fig. 171. The system is suspended by 
a phosphor bronze strip, and the coil can be adjusted by turn- 
ing the knurled knob at the top of the tube. A fine spring at 
the bottom serves to lead the current from the coil and oppose 
its motion. The advantage of this type of instrument over 
that of the Thomson form is, that it is not affected by the 
earth's or other external magnetic fields, so that it may be 
used in close proximity to dynamos. This principle is used in 
the construction of the Weston instruments, ^\^\ 208 and 235. 



Fig. 171.— Details 
of Removable Sus- 
pension Coil and 
Tube. 



GALVANOMETERS. 183 

QUESTIONS. 

1. State how you would proceed to measure the current flowing 
through a number of incandescent lamps with a long coil, high re- 
sistance galvanometer. 

2. The sensibility of a certain galvanometer is four megohms. What 
is meant by this statement ? 

3. Give two general classifications of galvanometers : first accord- 
ing to the principles employed in their construction ; second, accord- 
ing to their construction. 

4. Upon what factors does the sensibility of a galvanometer de- 
pend? 

5. Why is it necessary to construct such very sensitive instruments ? 

6. What is meant by the absolute calibration of a galvanometer? 

7. What advantage does a dead-beat galvanometer possess over one 
that is not so constructed ? 

8. Explain the difference between a differential and a ballistic gal- 
vanometer. 

9. Give three methods of damping the needle of a galvanometer. 

10. How would you arrange a low resistance sensitive galvanometer 
so that it could be used for measuring electrical pressure ? 

11. Explain how a galvanometer can measure electrical pressure, 
since the deflection of its magnetic system is dependent upon the 
strength of the current actuating it. 

12. What are the advantages of a D' Arson val galvanometer? 

13. Make a sketch of a double coil astatic galvanometer with the 
coils joined in parallel. Show the direction of current around the 
needle, and indicate the direction in which the system will be de- 
flected by the current. 

14. Why is an astatic galvanometer more sensitive than one with a 
single needle? 

15. An unknown current deflects the needle of a tangent galva- 
nometer 27 degrees ; the galvanometer constant is .65. What is the 
strength of current in amperes flowing through the instrument ? Ans. 
.33 ampere. 

16. In question 15 how many amperes will deflect the needle of the 
galvanometer 38 degrees? Ans. .507 ampere. 

17. A current of 5 amperes is sent through the galvanometer in 
question 15. What will be the corresponding deflection of the 
needle? Ans. 82°. 

18. Make a diagramatic sketch of the coils of the student's galva- 
nometer, similar to those depicted in Fig. 160, when it is connected : 
(1) two coils in series, two groups in parallel ; (2) one coil in series, 
with two in parallel and the remaining coil in series with them. 



LESSON XVII. 



ELECTROMAGNETS. 



Magnetisation of Iron and Steel by an Electric Current — Magnetic 
Field of an Electromagnet — Attractive Force of a Solenoid for an 
Iron Core — Magnetic Circuits—Typical Forms of Electromagnets, 
their Construction and Use — Magnetising Force, Ampere-Turns 
— Reluctance — Coarse and Fine Wire Electromagnets— Testing 
the Attractive Force of an Electromagnet — Magnetisation Curve — 
Tractive Force of an Electromagnet — Table XIII. Tractive Force 
and Magnetic Induction — Questions. 

192. Magnetisation of Iron and Steel by an Electric 
Current. — 

Exp. 59 : Wind a number of turns of insulated wire around an iron 
bar, Fig. 172, and send a current through the wire. Plunge the bar 
into iron filings, and it attracts them mostly at the ends, and when 
the current is interrupted the filings drop off. Test the polarity of 
each end of the bar with a compass. Note that upon looking at the 
end of the bar which repels the N-pole of the compass the current 
flows around the winding in the opposite direction to that in which 

the hands of a watch move. Fig. 172. 
When viewing that end which attracts 
the N-pole of the compass, the current 
flows around the wire in the direction 
that the hands of a watch move. Figs. 
172 and 173 illustrate the polarities of a 
steel bar, according to the clock rule, for 
all possible changes in either the direc- 
tion of current or the direction of wind- 
ing with a given direction of current. 

Exp. 60 : Eemove the bar from the 
coil and note that the polarity of each 
end of the helix is the same as with the 
bar inside of it ; the magnetism was, 
however, much stronger when the bar 
was inserted in the coil. If suspended 
or poised, see Fig. 148, the helix and its 
iron core will take up a position in the earth's field similar to the 
helix or compass needle. It will also attract or repel the poles of a 
like helix and core according to the law of attraction and repulsion. 

When a piece of hard steel is placed in the vicinity of an 
electromagnetic field, many of the lines of force of the field 
184 




Fig. 172. — Current Anti- 
Clockwise— N-Polarity. 



ELECTR OMA GNETS. 



185 




Fig. 173.— Current Clock- 
wise — S-Polarity. 



are bent out of their natural direction and converge into the 
steel. There are now more lines of force passing through 
the space occupied by the steel than when this space was 
occupied by air alone. The capability 
of any substance for conducting mag- 
netic lines of force is termed its per- 
meability, therefore the permeability 
of the steel is much greater than 
that of air. When a piece of soft 
iron is substituted for the steel, 
even more lines of force will pass 
through the same space, showing 
that the permeability or conducting 
power of iron is greater than that of 
steel. The permeability of iron may 
be as high as 2000 times that of air, 
or 2000 times as many lines of force 
will pass through space when occupied by iron as when it is 
occupied by air. An iron bar inserted in a helix or solenoid 
is a much better conductor of the magnetic whirls inside the 

solenoid than the air, so that the 
strength or attractive force of the 
solenoid is materially increased, 
though the magnetising current 
is the same as before. An iron 
core introduced into a solenoid 
carrying a current becomes strongly 
magnetised, and is called an electro- 
magnet. The direction of the 
lines of force through the iron 
core of the solenoid is the same 
as their natural direction through 
the solenoid alone, so that all the 
laws for polarity of the solenoid 
given under electromagnetism, 
Lesson XV, apply also to an 
electromagnet. By applying the 
principle of the molecular theory 
of magnetism, % 26, the phe- 
nomenon of magnetism in the iron bar produced by the mag- 
netic effect of the current will be understood. The current's 
natural magnetic field acts inductively upon the molecules of 




Fig. 174.— Magnetic Field of 

a Solenoid and Core. 
Made with iron filings on a hori- 
zontal piece of cardboard. 



186 PRACTICAL ELECTRICITY. 

the iron bar, causing them to change the relation of their 
internal magnetic circuits with respect to each other, thus 
producing an external field near the ends of the core, very 
much in the same way that a permanent magnet acts on 
them. The current's magnetic field simply makes evident 
the latent magnetism of the iron. This molecular action also 
accounts for the permanent magnetism produced in a piece 
of steel inserted in a solenoid after the current ceases, since 
the internal molecular friction prevents many of the mole- 
cules from resuming their original positions. 

193. Magnetic Field of an Electromagnet. — The graph- 
ical field of a solenoid and core, or straight bar electromagnet, 
would be similar to that of a solenoid alone, as in Fig. 151, 
except that the filings would be attracted more closely 
together, illustrating the greater density or number of lines of 
force due to the iron core. A compass needle, used to ex- 
plore the field, will take up the same position as with the 
solenoid alone, but it is now affected at a much greater dis- 
tance. The magnetic lines of force emanate from the N-pole 
of the bar electromagnet, and completing their path through 
the external medium enter the magnet again at its S-pole. 
If the iron core of the solenoid be pulled out somewhat from 
the coil and a field made, the magnetic lines are conducted 
further away from the coil before returning to it, as in Fig. 
174. The polarity is still the same as before, but the poles 
are not so strong as when the whole internal field of the sole- 
noid was composed of iron. 

194. Attractive Force of a Solenoid for an Iron Core. — 
When under the attractive influence of a solenoid, an iron 
bar is subjected to a pull, the magnitude of which depends 
upon the relative position of the two bodies and the magnetis- 
ing current. If either body is free to move, and the force 
sufficiently strong, it will move to accommodate through 
itself the greatest possible number of lines of force. This 
attractive force may be weighed by arranging the core upon 
one end of a balance arm, with the solenoid directly below it, 
and placing weights in the scale pan to balance the force of 
the current's field upon the iron. While balanced, as in 
Fig. 175, test the polarity of the bar by a compass, and it is 
magnetised by induction, ^[ 36, with the polarities as shown. 
Note that part of the magnetic lines from the solenoid com- 
plete their circuit through the core, entering at its upper end, 



ELECTRO MA GNETS. 



187 



Soft Iron 



which is consequently S-polarity (S where line3 enter), they 
emanate from the lower or N-end and pass through the coil. 
Place the solenoid nearer to the core, or lower the core to it, 
and the pull is 
considerably in- 
creased, as noted 
by the additional 
weights required to 
be added to bal- 
ance the current's 
attractive force. 
The strongest pull 
will take place 

when the middle of the iron core nearly 
coincides with the middle of the solenoid, 
as when they coincide the greatest number 
of the current's magnetic lines are accom- 
modated through the core. The term 
"sucking coil " is sometimes applied to the 
solenoid when used in such connection 




U'cijht 




Fig. 175. — Weighing 
the Magnetic Attrac- 
tion of a Solenoid for 
its Iron Core. 



Automatic Cir- 



cuit Breaker. 



When the current becomes 
excessive the magnetic field 
of the few series turns of wire 
attracts a solenoid which re- 
leases a spring and the switch 
opens. 



with its core. This 
principle is exten- 
sively used to oper- 
ate the feeding 
mechanism in arc lamps, Fig. 177 ; to 
automatically open switches in electric 
circuits when the current becomes ex- 
cessive, as in the circuit breaker, Fig. 
176, and in commercial instruments 
for measuring current and pressure, 
as in Fig. 191. 

195. Magnetic Circuits. — A 
simple magnetic circuit, ^j 42, of uni- 
form cross-section is represented by 
the solid iron ring in A, Fig. 178, 
around which a number of turns of 
insulated wire have been wound. 
The direction of the current and re- 
sulting polarity of the coil is shown, 
while the arrows indicate the direction 
of the lines of force around the ring, 
which is the same as that in which the 



188 



PRACTICAL ELECTRICITY. 




Fig. 177.— Pair of 
Solenoids with Iron 
Yoke and U-Shaped 
Movable Core. 



hands of a watch move. If a ring, so magnetised, be plunged 
into iron filings it will not show any external poles, since the 
magnetic lines have a complete circuit through the iron. When 
a small air-gap is made by sawing out a small section of the 
ring, B, Fig. 178, a compound circuit is formed, and the lines of 
force are compelled to pass through the air gap to complete 
their circuit, so that a strong N and S-pole is produced where 
the cut has been made, and the space is permeated with lines of 
force. 'The lines of force through the iron 
circuit are not nearly so dense as before, since 
the resistance of the circuit has been in- 
creased, and with the same magnetising force 
the magnetic lines diminish as the resistance 
of the circuit increases, just as in an electric 
circuit the current decreases when with a con- 
stant pressure the resistance is increased. If 
the removed section of the ring is now re- 
placed and the ring again plunged into iron filings while the 
core is magnetised, a great many filings will be attracted at 
the two joints, thus illustrating magnetic leakage. The density 
in the ring is not now so great as when it was solid, since the 
joints offer opposition to the magnetic lines, as is shown by 
some lines being forced through the air across the joint. A 
ring with two poles is shown in C, Fig. 178, the winding 

being in the 
same direc- 
tion through- 
out the ring, 
and the ends 
of the wire 
being joined 
together. 
Current is 
passed 




m 



A B 

Fig. 178. — The Magnetic Polarity of an Iron Ring 

from any point and flows around each half of the ring in an 
opposite direction to a diametrically opposite point and then 
back to the battery. The arrows indicate the direction of cur- 
rent and magnetic lines of force, from which it will be seen 
that a consequent N-pole is produced at the top of the ring and 
a S-pole at the bottom. The lines of force complete their path 
through the air from pole to pole, as will be noted by plunging 
the ring into iron filings. 



ELECTR OMA GNETS. 



189 




Fig. 179 



Exp. 61: Connect a horseshoe electromagnet, Fig. 179, with a 
source of current so that the limbs are like poles. Attract the keeper 
and then plunge the magnet into iron filings. One pole is produced 
in the centre of the keeper and the opposite pole in the bend of the 
horseshoe. The magnetic distribution is similar to the solid ring 
Avith two poles in C, Fig. 178. 

196. Typical Forms of Electromagnets, Their Con- 
struction and Use. — If the bar electromagnet, Fig. 172, is 
bent around into a U shape, as in the right-hand view of 
Fig. 179, it forms 
a horseshoe elec- 
tromagnet, there- 
by increasing the 
attractive power, 
IT 18. Instead of 
winding the in- 
sulated wire di- 
rectly upon the 

,, i Fig. 179.— Horseshoe Electromagnets with Keepers, 

erally wound 6 

upon a wooden or brass bobbin several layers deep, which is 
then slipped over the soft iron horseshoe core, as in the left- 
hand view of Fig. 179. The spools are then connected by 
wires so that the current will flow around each spool in the 
opposite direction, as viewed from the end of the core, when 
the limbs will have opposite polarity, Fig. 180. The at- 
tractive force of the magnet 
may be tested by means of a 
keeper of the same cross- 
sectional area, provided with a 
handle or hook and is found 
to be quite strong between the 
poles of the electromagnet. In- 
stead of a forged horseshoe it 
may be composed of three 
parts, as in Fig. 180, where the 
two iron cores or limbs are 
connected by an iron yoke of 
equal cross section and secured by machine screws. The 
direction of current and resulting polarity are also illustrated. 
Horseshoe electromagnets are used in many practical appli- 
cations of electricity, as in electric bells, automatic gas light- 
ing burners, electric locks, etc., and are designed and con- 




u& 



TKJ 



Fig. 180. — Direction of Current 
Around Horseshoe Magnet. 




8. Called a "Paradox. 
The rounded end has 
greatest tractive power. 



J2. Variay Duplex Mag-net. 






9, Magnetic Pop Gun. «0. Typical Two- Pole Magnet. 

Fig. 181.— Typical Forms of Electromagnets. 



11. Steven's and Hardy's 
Plunger Magnet. 



190 



ELECTR OMA GNETS. 



191 




Fig. 183.— Electromagnet with 
the Coil on the Yoke. 



structed to meet special requirements, according to the par- 
ticular work to be performed by them. When it is desired 
to construct an electromagnet that will respond quickly to a 
current of short duration, as in bells and telegraph sounders, 
the bobbin windings and cores are made as short as possible. 
To give a very powerful attraction at a short distance, a short 
cylindrical bar magnet surrounded by an outer iron tube and 
united at the bottom by an iron yoke, No. 4 and 5 A of Fig. 
181, is a good form ; the iron 
jacket forms a return path for 
the lines of force and the poles 
are concentric. This type is 
known as an ironclad electromag- 
net, and is adapted for lifting 
purposes in factories, etc., since 
the windings are well protected 
and not liable to be injured by 
rough usage. To attract iron 
across a wide air gap requires 
a horseshoe electromagnet with 
comparatively long limbs to accommodate the windings, 
because it requires a great many turns of wire to provide 
sufficient exciting power to drive the lines of force through 
the air. To obtain a gentle pull over a long range, a 
solenoid or long tubular coil and a long movable core is used, 
as in Figs. 175, 177, and No. 6 and 11 of Fig. 181. For 
nearly all purposes the iron parts, including the yoke and 
keeper, should be arranged to form as nearly as possible a 

closed magnetic circuit, 
as in No. 2, Fig. 181. 

In No. 7 of Fig. 181, 
the winding is contained 
on a bobbin mounted on 
one spool. As much 
wire is required as if two spools were used, but one bobbin is 
saved. To be efficient the wire should be close to the iron core 
so that it may be brought under the inductive influence of as 
many of the current's magnetic whirls as possible. In Fig. 
183, the solenoid is slipped on to the yoke, which is provided 
with short, stumpy pole pieces, for some specific purpose. A 
magnet with a slightly rounded or chamfered pole has an 
increased attractive power, since the lines of force become 




Fig. 184.— Straight Wire Electromagnet. 



192 PRACTICAL ELECTRICITY. 

very dense at the pole when they are thus slightly reduced, 
No. 8 of Fig. 181. In the electromagnet, No. 12 of Fig. 181, 
bare wire is used for winding, instead of insulated wire, but 
between each convolution is wound a silk or cotton thread 
to insulate the turns. The wire and thread are wound sim- 
ultaneously by a specially constructed machine and known 
as Varley duplex winding. The layers are insulated from 
each other by paper, the advantage being that since the 
thickness' of the insulation between the adjacent turns is 
greatly reduced by this method, many more turns per layer 
may be obtained than with ordinary winding, thus produc- 
ing a greater magnetising force. To produce magnets of 
equal strength one-third of the weight of copper is saved by 
using the duplex winding in comparison with the ordinary 
winding. 

A simple straight wire electromagnet is shown in Fig. 
184, the indicated polarity of which should assist in fixing 
clearly in the student's mind the direction of the magnetic 
whirls of a straight wire. A piece of one-eighth inch 
diameter iron gas pipe is sawed into two equal sections 
lengthwise and a straight wire carrying a current is placed 
in one section, as shown in Fig. 184. Looking in the 
direction the current is flowing the whirls are clockwise, 
so that the lines of force enter the lower edge of the pipe 
(consequently it is S-polarity) and emanate from the 
upper or N-edge. When dipped into iron filings they form 
an arch between the poles, as in the case of a horseshoe 
magnet, and many more filings are attracted than at the part 
of the wire not so surrounded with iron. The polarity will 
be reversed by reversing the current. If the other half of 
the pipe is used as a keeper it will be readily attracted 
when the current is sufficiently strong, forming a closed mag- 
netic circuit around the wire. The wire now passes practi- 
cally through a straight tube, and when again dipped into 
filings considerable leakage will be shown at the two joints. 

197. Magnetising Force, Ampere-Turns. — 

Exp. 62 : Connect the coils of an electromagnet wound with many 
turns of wire in series with another magnet wound with a few turns 
of wire and join them to a battery. Plunge each magnet into iron 
filings. The magnet wound with many turns attracts more filings, yet 
since they are in series the current strength is the same through each 
magnet. The magnetism depends upon the turns, as well as upon the 
current strength. 



ELECTR OMA GNETS. 193 

Exp. 63 : Note the number of pounds required to detach a keeper 
from the poles of its magnet when the spool is wound with 400 turns 
of fine wire and 1 ampere is passed through it, say 18 pounds is re- 
quired. Now substitute another spool wound with 40 turns of much 
larger wire through which 10 amperes are sent. The keeper is de- 
tached by a force of 18 pounds as before. 

A very weak current circulating a great many times around 
an iron core will produce the same magnetising force, or pounds 
pull, as a much larger current flowing only a few times 
around the core. The magnetising force of a solenoid, or any 
coil of wire, is directly proportional to the strength of current 
and the number of times it flows around the coil, but is in- 
dependent of the number of lines of force set up by it, 
which latter will depend upon the nature of the magnetic 
circuit. Magnetising force may be expressed in ampere-turns ; 
1 ampere-turn being 1 ampere flowing once around a coil of 
wire, or -J- ampere flowing around 2 turns, etc. 

To Find the Total Magnetizing Force of a Coil : 

Multiply the number of turns upon it by the strength of current 
passing through it. 

For example : four amperes circulating 25 times around 
a coil produce a magnetising force of 100 ampere-turns. The 
same force could be produced by 2 amperes and 50 turns, 
or 100 amperes and 1 turn, or 100 turns and 1 ampere, or 
1000 turns and one-tenth ampere, etc., the product of the 
turns and current in each case being 100. 

Let C = current in amperes ; 
T = number of turns. 

Then, 

Magnetising Force = C X T (54). 

AlgoC = MagaefeingJWe (55) 

T Magnetising Force (56). 

198. Reluctance. — The magnetising force or magnetomotive 
force, as it is called, is the force set up by the ampere- turns, 
which drives the magnetic lines, or magnetic flux, through the 
magnetic circuit, just as an electromotive force causes a current 
of electricity to flow through an electric circuit. A magnetic 
circuit offers a resistance, called reluctance, to the magnetic 
lines, and this reluctance must be overcome by the magnetis- 



194 



PRACTICAL ELECTRICITY. 




Fig. 185.— The Dotted Centre 
Line Represents the Mean 
Length of the Mag- 
netic Circuit. 



Induction 



ing force before induction is invoked. The number or density 
of lines of force per square inch of the circuit is called the 
induction per square inch and corresponds with the current 
in an electric circuit. It depends upon the magnetising 
force and reluctance. The length of 
the magnetic circuit in Fig. 185 is 
shown by the dotted line. The re- 
luctance of all non-magnetic bodies is 
practically the same, and when any 
such are interposed in a magnetic cir- 
cuit the number of lines of force is 
greatly diminished. In magnetic cal- 
culations the magnetising force of the 
circuit is divided by the magnetic 
reluctance of the circuit to obtain 
the magnetic density, and by adopt- 
ing units for the terms force, reluct- 
ance, and density, calculations are made similar to those 
used in an electric circuit, but are more complex. 

Magnetising Force 
Reluctance 

To force one unit line of magnetic force through an air 
path 1 inch long and 1 square inch in cross-section we must 
apply a magnetomotive force (M. M. F. ) of .15 ampere- 
turn. 

To force one unit line of force through one inch of soft iron 
of equal cross-sectional area requires a M. M. F. of only .00208 
ampere-turn, or, the air has about 1200 times the magnetic 
reluctance of soft iron. Iron may be magnetised so that 
there are 120000 lines of force per square inch. To produce 
this value in the above air gap would require, therefore, .25 
multiplied by 120000 or 30000 ampere-turns. The reluc- 
tance of a good magnetic joint is equal to about 8 inches of 
iron having the same cross-section. 

Prob. 71 : One thousand feet of wire are wound on a magnet coil. The 
average length of one turn is 3 inches. A current of 5 amperes is passed 
through the coil. What is the magnetising force ? 

By Formula (54) Magnetising Force = C X T = 5 X 4000 = 20000 
ampere-turns. 

1000 feet X 12 = 12000 inches, ^^° = 4000 turns, 

o 

current = 5 amperes, 3 inches — length of 1 turn. 



ELECTR OMA GNETS. 



195 



199. Coarse and Fine Wire Electromagnets. — Although 
the same results may be accomplished by using coarse wire 
magnets as those wound with much smaller and more expen- 
sive wire, each type has its advantage according to the way 
in which it is to be used. For example, the magnets of ah 
electric bell, telephone, or telegraph instrument are wound 
with fine wire and located at a considerable distance from the 
battery, so that there may be only a fraction of an ampere 
through the line. The line can thus be small in area when 
the magnetising force, ampere-turns, will be produced by a 
small current and thousands of turns. If it is desired to 
operate a small electromagnet from an electric light circuit, 
it is wound with very fine wire, so that its resistance will be 
high enough to permit it to be inserted in the circuit without 
heating. The current taken from the line will also be small 
in this case and the operation of the magnet inexpensive. 
On the other hand, if a coarse wire magnet had been used in 
this latter case, the same magnetic pull would have been ob- 
tained by using more current, and at an increase in the cost 
of operation. When the electromagnet is to be used in series 
with a line carrying current, as in a series arc lamp, a circuit 
breaker, or a street-car controller, the wire is made large and 
of low resistance, so as not to obstruct the flow of current, 
since the whole current passes 

through the coil, and the magnetis- 
ing force is then produced by a 
large current and a few turns. 

200. Testing the Attractive 
Force of an Electromagnet. — The 
magnetism of an electromagnet in- 
creases as the current through it 
is increased, up to the saturation 
point (see ^[29), but is not directly 
proportional to the current; that 
is, if one ampere, through a certain magnet requires a 
force of 56 pounds to detach its keeper (see test below) when 
2 amperes are passed through it, twice the force, or 112 
pounds, is not required, but usually much less. To make a 
test of the effect of different current strengths upon the 
attractive power, the magnet and keeper may be arranged in 
connection with a spring balance and windlass, as shown in 
Fig. 186. When the crank is turned the pounds pull may be 




Fig. 186.— Testing the Attractive 
Force of an Electromagnet. 



196 



PRACTICAL ELECTRICITY. 



noted till the detachment of the keeper takes place. A test 
made in this manner upon a small soft iron core electro- 
magnet, wound with 500 turns, and a soft iron keeper gave the 
following results when different current strengths were passed 
throught it. 

Test of the Attractive Force of an Electromagnet. 



Amperes. 


Pounds 


Magnetising force 


pull. 


Amperes X turns. 


1 


56 


500 


2 


72 


1000 


3 


80 


1500 


4 


86 


2000 


5 


90 


2500 


6 


93 


3000 


7 


95 


3500 


8 


96 


4000 


9 


96 


4500 



With a current of 1 ampere (500 ampere-turns), 56 pounds 
pull were required to detach the keeper ; upon doubling the 
current, instead of doubling the attractive force of the magnet 
to 112 pounds, it was only increased to 72 pounds, and with 
triple the current and magnetising force the attractive force 
was represented by 80 pounds. It will be noted also that the 
gain for each additional ampere is not the same, in the first 
instance being 16 pounds for the second ampere increase, 8 
pounds increase for the third, and 6 pounds for the fourth 
ampere, and so on. Finally 8 amperes produce the same 
amount of attraction as 9 amperes, so that all the molecules 
have been brought under the inductive influence of the cur- 
rent, or the saturation point of the iron has been reached. 
If 86 pounds attractive force is produced above with a current 
of only 4 amperes, it will not be practical to use twice as 
much current to obtain a gain of only 10 pounds. 

If the current be now gradually decreased from 9 amperes 
to 8, to 7, etc., the pounds pull is a little greater for each 
corresponding current than in the above test, since all the 
molecules of iron do not turn back to their original position 
after being magnetised. Thus, with ampere we would have 
the pull due to the residual magnetism, ^| 30. If a cast-iron 



ELECTROMAGNETS. 



197 



or hard-steel keeper had been used in the above test, each 
would have given a different set of results lower in value than 
those given, although the current and turns remained- un- 
changed. This is due to the different reluctances of these 
bodies, permitting less magnetic lines to travel through them 
than through the soft iron. 

201. Magnetisation Curve. — Unlike the constant resist- 
ance offered by a piece of copper to different strengths of an 
electric current, the reluctance of a piece of iron varies with 
each density of the lines of force accommodated through it, 
and this variation bears no constant ratio to the number of 
lines of force passing through it. For this reason curves of 
magnetisation are constructed for different specimens of iron, 
showing the relation of the induction to the magnetising 
force at different stages of magnetisatiou. In the curves 
shown in Fig. 187, the values representing the ampere-turns 
are laid off proportionally on the horizontal line and the re- 
sulting magnetisation plotted -to scale on the vertical line. 
Horizontal and vertical lines are drawn from each of the 
corresponding points and an X placed at their intersection. 
Lines drawn to connect the X's form a continuous line 
or curve, which represents the magnetisation. The curve 
gradually slopes upward 
with each increased exciting 
current until the saturation 
point is reached, after which . 
any further magnetising 2 
force does not produce an g 
increase in the induction as g 
will be noted by the curve 
sloping off to the horizontal. 

202. Tractive Force of 
an Electromagnet. — The 
following table gives the 
relation between pounds Flg ' w - Ml «^J}SZ 

pull Of an electromagnet for with a glven magnetising force in ainpere- 
each SQUare inch area of turns the relative induction may be 

, V- . . found from the curves. 

the poles in contact with 

the keeper and the number of lines of force per square 
inch. It is given so that the student may form some 
idea of the attractive force of a piece of iron. When it is 
stated, for example, that iron is magnetised to 45000 lines 

























^ 


EAL 


r D l 


HUN 








/ 


■< 








X 


^> 






/ 


1 








^ 


\> 
















/4 


















/ 














i 






"ti 


,51 






*?* 


^ 




/ 










ft> 


&* 








[> 





















10 20 30 40 

MAGNETISING FORCE. 



198 



PRACTICAL ELECTRICITY. 



per square inch, this means that if it were in the form of a 
horseshoe, the poles of which had a total area of one square 
inch, it would require a force of 28 pounds to detach the 
keeper. It will generally he a little less than the values 
given, since allowance must he made for magnetic leakage 
between the limbs and the resistance between joints.' The 
lifting, or adhesive power of an electromagnet is called its 
tractive poiver, or simply traction. 



Table XIII.— Tractive Force and Magnetic Induction. 



Magnetic lines of force 
per square inch. 


Tractive or lifting force. 

Pounds per square 

inch. 


6450 


.577 


12900 


2.308 


19350 


5.190 


25800 


9.228 


32250 


14.39 


38700 


20.75 


45150 


28.26 


51600 


36.95 


58050 


46.72 


64500 


57.68 


70950 


69.77 


77400 


83.07 


83850 


97.47 


90300 


113.1 


96750 


129.7 


103200 


147.7 


109650 


166.6 


116100 


186.8 


122550 


208.1 


129000 


230.8 



Suppose 40 pounds are required to detach a keeper from its magnet 
and that the total area of the poles is 2 square inches, what is the den- 
sity in lines of force per square inch ? First find the pounds tractive 
force per square inch, which equals 40 divided by 2 or 20 pounds per 
square inch. From the table we note that the magnetic density in lines 
of force per square inch corresponding to a tractive force of 20 pounds 
is 38700. From the above table we see that an electromagnet is capable 
of lifting 200 pounds for each square inch of cross-section when suffi- 
cient magnetisation is used, and before the saturation limit is reached, 
and that the lifting power may be directly increased by increasing the 
area of contact and working the iron at the same density per square 
inch. 



ELECTROMAGNETS. 199 

QUESTIONS. 

1. The pole of an electromagnet having a soft steel core deflects a 
compass needle 44 degrees when held at a distance of one foot. A soft 
iron core is substituted for the steel and the deflection is now 58 de- 
grees. How do you account for this, since neither the distance nor 
the current strength is altered ? 

2. Define magnetic permeability. 

3. Which magnet core mentioned in question 1 possesses the greater 
permeability ? 

4. What is the difference between an electromagnet and a solenoid ? 

5. Give an original application of the solenoid and core. 

6. Wind a steel key ring with insulated wire so that when a cur- 
rent is sent through the windings the ring will possess two diametrically 
opposite poles. Illustrate by sketches the direction of winding, direc- 
tion of current, and direction of the magnetic lines of force. 

7. What kind of poles are produced in the key ring in question 6? 

8. Explain and illustrate by sketches the economy obtained by 
using a duplex-wound magnet instead of one ordinarily wound. 

9. An electric bell wound with few turns of low resistance wire is 
located ten miles from the push button and batteries, but fails to ring 
when its circuit is complete, the batteries being in good condition and 
properly connected. What change would you make in the bell to 
correct the defect ? Why? 

10. What is reluctance ? 

11. How does the magnetic reluctance of air compare with that of 
iron? 

12. An electromagnet connected in series with some incandescent 
lamps connected in parallel, increases the resistance of the circuit ab- 
normally though it possesses the proper number of pounds pull. What 
change in connections and construction would you suggest so that the 
magnet would still possess the same lifting power and the lamps burn 
at their proper candle power ? 

13. A certain electromagnet possesses an attractive power of 37 
pounds per square inch, due to a current of 5 amperes. Would you 
expect the magnet to have double this attractive force per square inch 
when 10 amperes are passed through it ? Why ? 

14. The magnetomotive force of a solenoid is doubled. How would 
this affect the number of lines of force threading through it ? 

15. What is your answer to question 14 when the solenoid possesses 
a brass core ? A soft iron core ? 

16. It requires 60 pounds to detach a keeper from a certain electro- 
magnet and 74 pounds for an exactly similar magnet and current 
strength except that the poles are slightly rounded or chamfered. 
Why is this ? 



LESSON XVIII. 

AMMETERS. 

Measurement of Current Strength, Ampere-Meters — Gravity Amme- 
ter—Connecting Ammeters in Circuit — Balance Beam Amme- 
ter—Thomson .Inclined Coil Ammeter— Weston Ammeter — 
Weston Ammeter Shunt — Questions. 

203. Measurement of Current Strength, Ampere Me- 
ters. — An ammeter which is the commercial name for ampere 
meter, is a galvanometer designed to show by direct reading 
the number of amperes of current flowing through any cir- 
cuit in which it may be inserted. The voltameters and tan- 
gent galvanometer previously described for measuring current 
strength are used in the laboratory for standardizing commer- 
cial direct-reading instruments, required for portable use or 
upon station switchboards. A great variety of ammeters 
have been invented, based upon the principles given in *[f 180. 
A good ammeter should have a very low resistance, so that 
very little of the energy of the circuit in which it is inserted 
will be absorbed by it: the needle should be dead beat, *f[ 189, 
and so sensitive as to respond to minute variations of cur- 
rent ; the scale divisions not cramped at either end of the 
scale, but even throughout ; and the accuracy of the instru- 
ment should not be impaired when in close proximity to 
powerful magnetic fields, as switchboard conductors or 
dynamos. Ammeters are divided according to their use, into 
two classes : ( 1 ) a 'portable type, generally of a high class of 
construction and accuracy, used for measurements of pre- 
cision, and (2) the switchboard type, in the construction of 
which such refinement of precision is not required. In some 
makes of both types the whole current passes through the am- 
meter, while in others the ammeter is shunted, % 209. The 
shunt may either be contained within the instrument case, or 
it may be external to the instrument. In the latter case 
special leads used in the calibration are furnished to connect 
the shunt with its instrument. Milliammeters are ammeters 
in which the scale is graduated to read directly in thou- 
sandths of an ampere. 
200 



AMMETERS. 



201 




Fig. 188.— Solenoid 
Gravity Ammeter. 



204. Gravity Ammeter. — In this simple type of amme- 
ter, the magnetising current overcomes the attraction of 
gravity for a piece of suspended iron. The current passes 
around a helix of heavy ivire, which is bent in the arc of a 
circle, Fig. 188. A soft iron core bent to the same arc is sus- 
pended, so that one end is free to be sucked up into the helix 
by the field of the magnetising current. A pointer attached 
to the movable iron core swings over the 
scale, and will assume a different position 
for each value of the magnetising current. 

The instrument is calibrated by insert- 
ing it in series with a laboratory standard 
and marking the value of each current 
passed through it on the scale correspond- 
ing to each position of the pointer. Sup- 
pose that when 10 amperes were sent 
through the helix the core was in such a 
position as to accommodate through itself 
the greatest number of the magnetic lines 
of the helix, then the limit of the scale 
was attained and the capacity of the instrument was to 10 
amperes. By attaching a small weight to the core, if the 
wire were of sufficient size to carry the current, the capacity 
could readily be made to 20 amperes. The division per 
ampere would, however, be about one-half as large. The ob- 
jection to this 
type of instru- 
ment is that the 
movement of the 
core is much 
greater at some 
positions than at 
others for the 
same increment of current, giving a scale of unequal divisions, 
and generally cramped at each end. The instrument is not 
dead beat, is readily affected by magnetic fields, and can 
only be used in a vertical position. 

205. Connecting Ammeters in Circuit. — Since the total 
current to be measured in any circuit must flow through an 
ammeter, an ammeter must always be connected in series with the 
circuit and between the generator and apparatus receiving the 
current, as in Fig. 189. Suppose the coil in a gravity 



m 



Ammeter 

DYAIAA/IO 



sa 



LAMPS 



Fig. 189.— Ammeter Correcfhj Connected in Series 
with the Circuit. 



202 



PRACTICAL ELECTRICITY. 



m 



i 



j 



_B_110_ 



Fig. 190. — Ammeter Incorrectly Connected in 
Parallel with the Circuit. 



ammeter has a resistance of . 1 ohm and that it is incorrectly 
placed in parallel with some incandescent lamps connected 
to a dynamo, Fig. 190. How much current w r ill flow 
through the ammeter if the pressure is 110 volts between the 

mains ? The current 
that would flow 
through the ammeter 
would be by Formula 

(28) 

1100 amperes or 
enough to totally de- 
stroy the instrument by 

excessive heating, since the current-carrying capacity of the 

wire would be far below this value, % 257. 

206. Balance Beam Ammeter. — In the form of ammeter, 

illustrated in Fig. 191, a horizontal beam is supported on a 

knife bearing. An iron core 

made up of a bundle of soft iron 

wires is suspended by a hook from 

one end of the beam and is 

balanced by a counterweight on 

the other end. The current to 

be measured is passed through a 

coil of a few turns of heavy wire 

located directly below the core, 

and attracts it, to a certain dis- 
tance, for each value of the cur- 
rent sent through the coil. A 

pointer attached to the beam 

swings over the scale, which is 

calibrated to read in amperes. A 

plumb-bob indicates when the 

instrument is properly leveled. 

The instrument depicted illus- 
trates a to 300 scale, and can be 

calibrated for a larger capacity, 

say to 400 amperes, by sliding 

the counterweight along the beam toward the right, when 

a greater magnetic pull than before would be required for 

each position of the core. A 150 ampere instrument, of this 

type, contains 6 turns of No. B. & S. copper wire, the resist- 




Fig. 191.— 
Ammeter 



Balance Beam Gravity 
— Westinghouse Type. 



AMMETERS. 



203 



accommodate 
itself the lines 
of the magnetism 




Fig. 192. — Thomson Inclined Coil Ammeter. 



ance of the instrument being about .0001 ohm. The instru- 
ment may be calibrated for an alternating or direct current 
circuit. 

207. Thomson Inclined Coil Ammeter. —In many types 
of ammeters, beside the above, the magnetic body is a 
piece of iron, rather than a magnet, and placed so that it 
will gradually move to 

through 
of force 
coil. 
The Thomson inclined 
coil ammeter utilizes this 
principle and is con- 
structed in the portable 
and switchboard pat- 
terns. A view of the 
portable type, with cover 
removed, is shown in 
Fig. 192, and a sectional 
view in Fig. 193. A cir- 
cular coil of wire, C, is 
mounted with its axis inclined to the horizontal. Through the 
centre of the coil is passed a vertical shaft mounted between 
jewel centres and carrying a pointer at its upper end. A small 
iron vane, A, is attached to the shaft at an angle, and the 
movable system is controlled by the two flat springs, S. 

When current is passed through 
the coil the vane tends to turn 
against the action of the springs, 
so as to become parallel to the 
lines of force indicated by the 
direction of the arrows. The 
turning of the shaft causes the. 
pointer, P, to sweep over the 
scale. The coils for large sizes of 
instruments are generally wound 
with a few turns of flat insulated 
copper ribbon having a very low resistance. These meters 
are adapted for use with alternating or direct currents. 

208. Weston Ammeter. — The construction of this instru- 
ment is based upon the principle of the D'Arsonval galva- 
nometer, ^| 191. A general view of a portable instrument is 




Fig. 193.— Construction of In- 
clined Coil Ammeter. 



204 



PRACTICAL ELECTRICITY. 




Fig. 194. 



-Weston Ammeter with Self- 
Contained Shunt. 



shown in Fig. 194, and interior views in Figs. 195 and 196. 
A permanent horseshoe magnet, M, is fitted with soft iron 

pole pieces, P P, Fig, 
197, between which a 
stationary cylinder of 
soft iron, C, is sup- 
ported by a brass piece 
extending across the 
pole pieces. The iron 
cylinder is smaller in 
diameter than the bore 
of the pole pieces, so 
that the magnetic lines 
of force pass across 
this air gap, making 
a very strong and uni- 
form magnetic field. 
The movable system 
is shown in Fig. 198. It consists of a rectangular coil of wire, 
wound upon a bobbin of thin sheet copper or aluminum and 
delicately suspended be- 
tween jewel bearings. 
The terminals of the coil 
are connected to the hori- 
zontal spiral springs, 
against which the coil 
acts when it tends to 
rotate, the springs serv- 
ing to also conduct the 
current to and from the 
coil. A thin aluminum 
knife-edge pointer at- 
tached to the bobbin and 
swinging over the scale, 
Fig. 195, indicates the 
angle of deflection of the 
coil. This coil is mounted 
concentrically with the 
iron cylinder and pole 
pieces in the air gap, as 
Shown in Fig. 196, where Fig. 195.-Weston Ammeter with Cover Re- 

. o .-I - i • moved Snowing D Arsonvai 

part 01 the pole piece, Galvanometer. 




AMMETERS. 



205 



etc. , have been cut away. When a current is sent through 
it, by the springs, the coil tends to move through the 
magnetic field, to take up a position so that its lines of force 
will be in the same direction as those of the field. It 
will so move until the torsion of the springs is balanced 
by the force tending to move the coil, when the pointer 
will indicate the angle of deflection. The angle of deflec- 
tion is nearly proportional to the current throughout the 
movement, which £-ives a very uniform scale, as can be seen 
from Fig. 195. The metallic bobbin on which the coil is 




Fig. 196. — Method of Mounting the Movable Coil in Weston Instruments. 

wound has an electromotive force induced in it, only while 
the coil is moving, which causes eddy currents, ^f 292, to 
flow around the bobbin in the opposite direction to the cur- 
rent in the coil. These momentary currents tend to stop the 
motion of the coil, and have the effect of preventing the 
needle from oscillating, thus bringing it to rest quickly at the 
proper position and making the instrument very dead-beat, 
^| 189. The movable coil is extremely light, the friction 
small, and the instrument very sensitive to minute variations 



206 



PRACTICAL ELECTRICITY. 



of current. A current of about .015 ampere will give a full 
scale deflection of the pointer. The instrument is carefully 
balanced, so that it may be used in a horizontal or vertical 

position. An ammeter, however, 
should always be calibrated in the 
position in which it is to be used; A 
mirror is located just below the scale 
of the portable instruments. By- 
looking clown on the pointer so that 
it is directly over its reflection in the 
mirror, errors in reading the scale 
divisions due to parallax * are thus 
avoided. In Weston instruments the 
post marked -f is the one by which 
the current should enter the instru- 
ment so that the coil will be deflected 
in the right direction. 
209. Weston Ammeter Shunt. — 
Only a small portion of the total current to be measured is 
sent through the movable coil, the remainder passing through 
a shunt, •[[ 162. The shunt is made of a special resistance 




Fig. 197.— The Magnetic Cir 

cuit of the Weston 

Instruments. 



§- 



alloy, and contained either in the in- 
strument, in a separate portable case, 
or on an external block, Fig. 199, as in 
the switchboard type of instruments. 
The lead wires to the shunt, the instru- 
ment and the shunt, are all numbered 
to correspond, so that when used 
together the indications agree with the 
calibration. The shunt leads should 
never be shortened, because the de- 
creased resistance in the shunt circuit 
would permit more current to flow 
through it, so that the indicated read- 
ings would be higher than the actual Coil, Springs and Pointer 
current flowing. The resistance of the of Weston Instruments. 



*The apparent angular displacement of an object when seen from two different 
points of view. 



AMMETERS. 207 

instrument and its shunt is very low, little energy, there- 
fore, being lost when it remains continually in circuit. A 
15 ampere shunted instrument has a joint resistance of .0022 
ohm. A number of shunts are sometimes furnished in a 
separate case for a single portable instrument, which is called 
a multiplier, and is used for increasing the range or capacity 
of the instrument. For example, with a shunt of .004 ohm 
in Fig. 199, suppose the coil receives sufficient current to de- 
flect the pointer entirely across the scale, and this deflection 
corresponds to 50 amperes in the main circuit. The differ- 
ence in pressure between the shunt terminals by Ohm's Law 
is equal to C X R = 50 X .004 = 0.2 volt. Now the shunt 
is reduced in resistance to one-half .004 or .002 ohm, and the 
pressure applied to the movable coil for the same current is 
equal to C X R = 50 X .002 = .1 volt, or the coil will receive 
only one-half the former current, and thus be deflected to the 
middle of the scale. _/wn 

The range of the am- 
meter is now to 100 
amperes, or each scale 
reading must be mul- 
tiplied by 2 to obtain 
the true value of the 
current when used 
with this shunt, In 
the same manner with Fig. 199.— Connections of an Ammeter with a 
a reduction of the Portable Shunt, 

shunt's resistance to one-third of its original value, the range 
is increased three-fold and the readings are multiplied by 3. 
One advantage of an external shunt in switchboard instru- 
ments for power stations is, that instead of running heavy 
copper cables to a distant ammeter, a shunt may be inserted 
in the cable circuit and the two small size shunt leads wired 
to the instrument, thus effecting an economy in copper and 
construction. A Weston ammeter may be used without its 
shunt as a millivoltmeter, in which case it is quite sensitive and 
adapted to many electrical measurements. When resistance 
is added in series with it, it becomes a long coil galvanome- 
ter, and may be calibrated as a direct reading voltmeter, 
If 180. The same mechanical construction is employed in 
Weston voltmeters, ^f^f 234 and 235, the only difference "being 
in the value of the extra resistance added and the method of 
connecting it to the instrument. 




208 PRACTICAL ELECTRICITY. 

To measure currents larger than the capacity of an ammeter. 
Let R = resistance of shunt required ; 
r — resistance of ammeter ; 
A = range of ammeter ; 
Ax = desired range of ammeter. 

Then,E = 5 ^ x xr (57). 

The indicated readings obtained must be multiplied by ~ l to be cor- 
rect. A 

Prob. 71-A: (1) What will be the resistance of a shunt required to 
increase the capacity of an ammeter from 150 to 600 amperes? Re- 
sistance of the instrument -.009. (2) What will be the multiplying 
power of the shunt ? 

By Formula (57) R = -~^ X r = * 50 1KA X .009 = .003 ohm. 
A x — A 000 — 150 

Multiplying power of the shunt = A 1 =r^ = 4, or by Formula (48) 

A lOO 

„ G, -, .009,, , 

QUESTIONS. 

1. What is the advantage of a Weston type of ammeter over one 
constructed to actuate upon the solenoid and core principle? 

2. In what respect does the Thomson inclined coil ammeter differ 
from the Westinghouse balance beam type ? 

3. An ammeter of 200 amperes capacity is required to be located 
50 feet from the main generator cables. What economy would be at- 
tained by using a shunt type of instrument in this case ? 

4. In a station shunt type ammeter a pair of shunt leads are used 
which are the same length as those furnished with the instrument, 
but of a smaller size. How will this affect the meter's indications? 

5. An ammeter with its leads has a resistance of 50 ohms, and 
the shunt, a resistance of 0.1 ohm. If 20 amperes are flowing through 
the shunt what current does the ammeter receive? Ans. 0.04 
ampere. 

6. In question 5, if 20 amperes are flowing through the circuit to 
which the shunted ammeter is connected, what current flows through 
the ammeter? Ans. 0.0399 ampere. 

7. A solenoid ammeter having a resistance of 0.5 ohm is incor- 
rectly connected in parallel with 10 incandescent lamps in parallel. 
Each lamp has a resistance of 220 ohms and requires 0.5 ampere. 
What current will flow through the ammeter when the circuit is 
closed ? Ans. 220 amperes. 

8. It is desired to use a solenoid ammeter of only 50 amperes ca- 
pacity in a circuit through which 150 amperes are flowing. How 
would vou do this ? .. , 

9. How much resistance would you add if the instrument m ques- 
tion 8 had a resistance of .06 ohm ? Make a sketch. Ans. 0.03 ohm. 

10. By what should the indications of the ammeter in question 9 
be multiplied in order to obtain the true reading ? Ans. 3 ? 



LESSON XIX. 

ELECTRICAL WORK AND POWER. 

Force— Different Kinds of Force— Mass and Weight— Work— Power 
— Horse Power of a Steam Engine — Difference Between Energy, 
Force, Work, and Power— Electrical Work — Electrical Power — 
Heat and Work — Equivalents of Mechanical and Electrical Work 
—Electrical Horse Power— The Kilowatt— The Watt-Hour and 
Kilowatt-Hour— Electrical Power Calculations— Electrical Power 
Formulae— Power from Cells — Efficiency of a Battery — Questions 
and Problems. 

210. Force. — Force is defined as that which produces mo- 
tion, or a change of motion or matter ; thus force must always 
be applied to any body to cause it to move. To increase, 
decrease, or stop this motion, that is to change it, force must 
again be applied. For example, to start a loaded wheel- 
barrow force must be applied, either by pushing or pulling it, 
but when it is set in motion less force Avill be required to keep 
it in motion ; to cause a change in motion, that is to increase 
or decrease the speed, extra force must be applied. Force 
does not always produce motion, but only tends to produce 
it, as when a man tries to push a laden freight car he applies 
all his muscular force, but no motion results. 

211. Different Kinds of Force. — There is the force of 
gravitation, in virtue of which all bodies free to move will fall 
from a higher to a lower level. The force exerted by a man 
riding a bicycle or a horse drawing a carriage are examples of 
muscular force. An engine draws a train of cars by reason of 
the mechanical force applied, which is due to the expansion of 
the steam in the steam cylinder. A mixture of air and illu- 
minating gas in a room is ignited and the explosion wrecks 
the room ; the action is due to the chemical force exerted. 
The force which produces or tends to produce a flow of elec- 
tricity is electromotive force. The force which sets up mag- 
netic lines of force is magnetomotive force. The rate at which 
a train moves depends upon the force exerted by the engine, 
so also, the rate of flow of electricity depends upon the amount 
of electromotive force applied. 

14 209 



210 PRACTICAL ELECTRICITY. 

212. Mass and Weight.— The mass of a body is the 
quantity of matter in it ; the weight of a body is due to the 
force of gravity acting upon this matter. Since the force of 
gravity diminishes as we ascend from the earth's surface, the 
attraction for a mass of matter will diminish, or it will weigh 
less on the top of a high mountain than at the sea level ; the 
mass of matter, however, would be the same in each case. 
Weight is not, therefore, the same thing as mass, but we can 
conveniently measure a body by its weight. 

213. Work. — Work is clone when force overcomes a re- 
sistance, or, work is force acting through space (W = F X S). 

Work = Force X Distance, 
or Work = Pounds X Feet = Foot-pounds. 

Work is not always done when a force acts ; for instance, 
a man pushes with all his force against a brick wall ; he is 
exerting force, but doing no work because no motion results, 
nor is any resistance overcome. If a weight be lifted, work 
is done directly in proportion to the weight and to the dis- 
tance through which it was moved. Thus, the work done in 
lifting 4 pounds to a height of 3 feet is equivalent to 12 foot- 
pounds of work. Exactly the same work is performed when 
2 pounds are raised 6 feet; or 6 pounds raised 2 feet ; or 12 
pounds raised one foot. Work does not always consist in 
raising weights ; the steam engine does work by hauling 
a train, due to the expansive force of steam acting upon the 
piston ;, an explosion of powder in a cannon causes an iron 
ball to traverse a certain distance. The chemical action in a 
cell sets up a force which causes a current to flow through an 
electric motor and the motor drives an automobile weighing 
so many pounds a certain number of feet every minute, 
hence the total foot-pounds of work are performed electrically. 
The work in each case is measured in foot-pounds. Whether 
work be done mechanically, chemically, thermally, or elec- 
trically, it can be expressed in foot-pounds. The total 
amount of work done is independent of time, that is, the 
same work may be performed in one hour or one year. When 
different amounts of work performed in different times 
are to be compared, then reference is made to the time, or 
rate of working, or the power. 

214. Power. — Power is the rate at which work is done, 
and is independent of the amount of work to be done. 



ELECTRICAL WORK AND POWER. 211 

-r, , , . , i • x Work Foot-pounds t- ± j 

Power (rate of working) = -^ = m = Foot-pounds per 

unit of time. TlME TlME 

For example, it requires four hours for a particular engine 
to draw a train from one station to another, while another 
engine may draw the same train the same distance in two 
hours. One engine is thus twice as powerful as the other, be- 
cause it can do the same work in one-half the time. When 
the train had reached its destination it would have repre- 
sented the same amount of work clone, no matter whether it 
had traveled at One mile per minute or one mile per hour, 
leaving, of course, friction and air resistance out of account. 

Power is estimated according to the amount of work done 
in a given period of time. As mechanical work is measured 
in foot-pounds, mechanical power would thus be so many 
foot-pounds per minute, or per second. The mechanical unit 
of power is the horse power. 

One mechanical horse power = 33000 ft. lbs. per 
minute, or 

— ^- n — = 550 ft. lbs. per second. 
bU 

If a body weighing 33000 pounds be raised one foot every 
minute then we have a rate of working equal to one horse 
power ; or if 16500 pounds be raised two feet per minute, 
the rate of working is the same, one horse power. If the work 
were continued at the same rate for one hour, we would have 
a larger unit of work, or the horse-power-hour. When we say 
that an engine is developing 40 horse power we mean that it 
is performing 550 X 40 = 22000 foot-pounds of work every 
second. 

215. Horse Power of a Steam Engine. — The horse pow- 
er of a steam engine may be readily calculated from data ob- 
tained from it while it is working. The mean pressure of the 
steam upon the piston is found by attaching a graphical 
recording indicator to the steam cylinder which shows the 
various steam pressures during a stroke of the piston. From 
this "card," as it is termed, the average or mean effective 
pressure throughout the stroke is obtained. The speed of the 
engine must be noted while the card is taken but the length 
of stroke in feet, and area of the piston-head in square inches 
should be previously obtained. 



212 PRACTICAL ELECTRICITY. 

The following formula may then be used to ascertain the 
rate of working, or horse power developed corresponding to 
the above conditions : 

p y T y A \/ M 

Horse power of a steam engine = — oonnn — • • (58). 

When P = mean effective steam pressure in pounds (from 
indicator card) ; 

L m= length of stroke in feet ; 

A = area of piston-head (in square inches) ; 

N = number of strokes per minute (twice the num- 
ber of revolutions). 

Prob. 72 : From an indicator card the mean steam pressure is 
45 lbs., the speed of the engine 275 revolutions, length of stroke 12 
inches, area of piston-head one-half a square foot. What horse power 
is developed by the engine ? 
_% Ferula (58) H.P. _ » X -LxA X » , « X IXgX ». 

P = 45 lbs., L == 12 inches = 1 foot, A = } sq. ft. = 72 sq. in. 
N = 275 revolutions X 2 strokes per rev. = 550. 

216. Difference Between Energy, Force, Work, and 
Power. — It is important that the student should thoroughly 
understand the meaning of the above terms. Energy is the 
capacity to do work. Force is one of the factors of work and 
has to be exerted through a distance to do work, the work 
being reckoned as the product of the force and the distance 
through which it has been applied. Work is done when 
energy is expended or when force overcomes a resistance. 
Power is the rate of working. 

217. Electrical Work. — Work is force acting through space, 
or energy expended, therefore, resistance is overcome when 
work is performed. Force may exist without work being 
performed, as when you push against a table and do not 
move it, no work is done, yet the force exists. An electrical 
force exists between the two terminals of a battery, tending 
to send a current of electricity from one to the other through 
the air. The force is not sufficient to overcome the resistance, 
of the air, therefore no current flows and the battery is not 
doing any work ; the same is true with a dynamo when 
running on open circuit. When a wire is connected across 
the battery terminals, the force overcomes the resistance of 
the wire and electricity is moved along, around or through 
the wire, which becomes heated. The electrical work, or 



ELECTRICAL WORK AND POWER. 213 

energy expended, is represented by the amount of heat gen- 
erated in this instance, ^j 257. With a small lamp connected 
to the battery, the work is represented by the heat and light 
given by the lamp as well as the heat given to the remainder 
of the circuit. The total work performed is the product of 
the force, the current, and the time that the current is main- 
tained, or 

Electrical Work =± Volts X Amperes X Time. 

The unit of electrical work is the amount of work performed by 
a current of one ampere flowing for one second under a pressure 
of one volt and is called a joule. 

Since an ampere flowing for one second is equal to one 
coulomb, 1| 116, a joule is, therefore, one volt-coulomb and is 
analogous to the mechanical unit of work, the foot-pound, 
which has no special name. The volt-coulomb is not so 
great as the foot-pound, however, 

1 joule = . 7375 foot-pound ; 
1 foot-pound = 1.356 joules. 
Larger units of electrical work are given in ^J 221. 

To Find the Total Electrical Work, in Joules, Per- 
formed in any Circuit : 

Multiply the volts causing the current to flow by the current and 
the time it flows , expressed in seconds. 

Joules = volts X amperes X seconds, 

or J = E X C X t •. . (59). 

When t = the time in seconds ; 
J = work in joules. 

Prob. 73 : A current of 20 amperes is maintained through a number 
of incandescent lamps for one hour by a pressure of 110 volts. How 
much electrical work has been performed ? 

By Formula (59) J = E X C X t = 110 X 20 X 3600 = 7920000 joules. 
E = 110 volts, C — 20 amperes, t = 60 X 60 = 3600 seconds. 

To Find the Total Electrical Work, in Joules, Per- 
formed in Any Part of the Circuit When the Current 
Strength and Resistance are Known : 

Multiply the square of the current by the resistance, and this 
product by the time the current flows. 

j = cxcxRxt, 

or J = C 2 XRXt (60). 



214 PRACTICAL ELECTRICITY. 

By substituting for E in Formula (59) its value C X R, we 
get Formula (60). Also by substituting the value of C, 
which equals E -j- R in Formula (59), we obtain an expres- 
sion to find work in joules when the volts and resistance are 
known. 

By Formula (59) J = E X C X t. 

Substituting, C = | then Jrz^xt, 

orJ = | 2 Xt (61). 

Prob. 74 : A current of 5 amperes is passed for one-half hour 
through an arc lamp, the resistance of which is 4 ohms, hot. How 
much energy has been expended ? 

By Formula (60) J = C 2 XExt = 5x5x4X 1800 = 180000 joules. 
C = 5 amperes, R = 4 ohms, t = £ hour — 1800 seconds. 

Prob. 75 : The resistance of the copper cables connecting a dynamo 
with its switchboard is .1 ohm, and 2 volts are required to send the 
full load current through them. How much energy is expended in 
10 hours ? 

By Formula (61) J = |xt = ^^ X 36000 = 1440000 joules. 

E = 2 volts, R = .l ohm, t = 60 X 60 X 10 = 36000 seconds. 

218. Electrical Power. — Power is the rate at which en- 
ergy is expended, and is independent of the total work to be 
accomplished. The rate of working, or the power is found 
by dividing the total work by the time required to per- 
form it. 

Electrical Power Electrical Work . 

The unit of electrical power is a unit of work performed in 
a unit of time, or a joule per second, and is called a watt. 
Therefore : 

w ±± work joules volts X amperes X seconds 

Watts = r- ==— r = 1 = 

time seconds seconds 

volts X amperes. 

One watt therefore equals one volt multiplied by one ampere, oi 
2 volts by .5 ampere, etc. 

1. To Find the Rate in Watts at which Energy is Ex- 
pended in a Circuit : 

Multiply the current in amperes by the pressure causing it to flow. 



ELECTRICAL WORK AND POWER. 215 

Let W = watts expended ; 

C = current in amperes ; 
E = pressure in volts. 
Then, watts = volts X amperes, 

W = E XO (62). 

2. To Find the Current when the Watts and Pressure 
are Known : 

Divide the watts expended by the voltage causing the current 
to flow. 

From Formula (62) W = E X C. 
Therefore, 

Amperes = ™ or C = f (63). 

3. To Find the Pressure when the Watts and Current 
are Known : 

Divide the ivatts expended by the current flowing. 

From Formula (62) W = E X C. 

Therefore, 

„ -,, Watts _ W ,n A \ 

Volts = -r orE = -« (64). 

Amperes C 

Prob. 76 : How many watts are consumed by one hundred incan- 
descent lamps connected in multiple to a 110-volt circuit, supposing 
each lamp to have resistance (hot) of 220 ohms ? 

C = p = son = 9 am Pere per lamp. 

W = E X C = 110 X \ = 55 watts per lamp. 55 X 100 = 5500 watts. 

Prob. 77 : What current is required to operate a 50- watt lamp on a 
100-volt circuit ? 

By Formula (63) c = ^ == ^ = ^ ampere. 
W^ 50 watts, E = 100 volts. 

Prob. 78 : A 500-watt motor requires a current of 10 amperes. 
What E. M. F. is necessary to operate it ? 
By Formula (64) E =^ = 500 = 5Q yoltg 

W = 500 watts, C = 10 amperes. 

219. Heat and Work. — One of the most important dis- 
coveries in science is that of the equivalents of heat and work : 
that is, that a definite quantity of mechanical work can always 
produce a definite quantity of heat, and, conversely, this heat, 



216 



PRACTICAL ELECTRICITY. 



if the conversion be complete, can perform the original quantity 
of work. 

All kinds of energy (chemical, mechanical, electrical, etc.) 
are so related to each other that energy of any kind can be 
changed into energy of any other kind. This statement is 
known as the doctrine of correlation of energy. ' When one 
form of energy disappears an exact equivalent of another 
form takes its place, so that the sum total of the energy is 
not changed. This is known as the doctrine of conservation 
of energy. These two principles constitute the corner-stone of 
physical science. 

220. Equivalents of Mechanical and Electrical Work- 
Dr. Joule, of England, was the first to ascertain the rela- 
tion existing between mechanical work, heat, and electricity. 








5 





Fig. 200. 



FAD&LE 

-Dr. Joule's Paddle Wheel Experiment. 



In an experiment he caused a paddle-wheel to revolve in a 
vessel filled with water, by means of a falling weight at- 
tached to a cord and wound around the axle of the wheel, 
Fig. 200. The resistance offered by the water to the motion 
of the paddles was the means by which the mechanical 
motion of the weight was converted into heat, which 
resistance raised the temperature of the water. From this 
experiment it was found that 778 foot-pounds of work would 
raise the temperature of 1 pound of water 1° Fahrenheit; 



ELECTRICAL WORK AND POWER. 217 

also by the doctrine, ^[219, the heat which would raise 1 
pound of water 1° Fahrenheit would also raise 778 pounds 1 
foot. The quantity, 778 foot-pounds, is called the mechanical 
equivalent of heat, or Joule's equivalent. If now we heat the 
pound of water by a current of electricity until its tempera- 
ture is raised 1° we will have done the same work electrically 
as was previously done mechanically. An apparatus similar 
to our calorimeter, ^f 112, would be suitable for this experi- 
ment. The current in amperes and the pressure in volts 
must be accurately read from instruments. 

From this experiment it was found that a current of 1 
ampere flowing through the coil for 1 second, under a pres- 
sure of 1 volt (or 1 watt expended) would do the same 
work as .7375 foot-pound expended in 1 second. The 
rates of working are thus equal since the same work in each 
case has been accomplished in the same time. Therefore : 

One watt = .7375 foot-pounds per second, 
or 1 foot-pound = 1.356 watts. 

Now since 550 foot-pounds per second are equivalent to 1 
mechanical horse power, ^| 214, an equivalent rate, of elec- 
trical working would, therefore, be : 

550 
7375 = 746 watts — 1 electrical horse power. 

A current of 1 ampere, and 746 volts, or 1 volt and 746 
amperes, etc., maintained through the calorimeter coil for 1 
second would heat the water to exactly the same temperature 
that it would be heated by the paddle wheels when, in 1 
second, 550 pounds fall through a distance of 1 foot, or 1 
pound falls through 550 feet, etc. If these rates of working 
are continued for equal periods of time, as an hour, or a day, 
the water is raised to the same temperature by either method, 
so that the total work performed is also the same. 

221. Electrical Horse Power. —From % 220, the method 
of obtaining the equivalent of a mechanical horse power in 
electrical units was given. The watt being a very small unit 
of power, the larger unit, an electrical horse power, is often 
used. 

To Find the Electrical Horse Power (H. P.) Main- 
tained in any Circuit, or Part of a Circuit : 



218 PRACTICAL ELECTRICITY. 

Multiply the volts causing the current to flow by the current 
expressed in amperes and divide this product by 7^6. 

tt p _ Watts volts X amperes E X C 

M - F * — 1W— ~~ 746 —"746 ' 

or H. P. =5^ (65). 

Prob. 79 : A dynamo maintains a pressure of 110 volts across an 
electric light circuit when the ammeter indicates 100 amperes ; what 
horse power is being developed by the machine ? 

-T»-n 1 /f.~\ TXT. EXC HO X 100 -, , ^ TT TT> 

By Formula (6o) H. P. = 746 == — sjg — = 14.7 H. P. 

222. The Kilowatt.— The kilowatt (abbreviated K. W.) is 
a larger unit of electrical power. One kilowatt equals 1000 
watts, or is about 1 J times as large as the horse power unit. 

iz-i t+ /-it wn Watts EXC .-.- 

Kilowatts (K.W.)= 3qoO = ~I000 ' ' ' (66) ' 
Watts = K.W.X 1000 (67). 

1 H. P. = 0.746 K. W. 

1 K.W. = 1.34H.P. 

Prob. 80 : What is the capacity in kilowatts of a generator carrying 
a load of 120 volts and 500 amperes ? 

D . , faa x rr ,,, E X C 120 X 500 _ A „ w 

By Formula (66) K. W. == 1Q0Q = — 100Q = 60 K. W. 

Prob. 81 : How many amperes will be maintained by a 40 K. W. 
dynamo at a pressure of 100 volts ? 

By Formula (67) Watts = K. W. X 1000 = 40 X 1000 =■ 40000 watts. 

W 40000 
By Formula (63) 0= w- = -. nA = 400 amperes. 

223. The Watt-Hour and Kilowatt-Hour.— The joule is 
a very small unit of electrical energy or work, so that larger 
units are generally used in practice. A watt-hour is one watt 
exerted or expended for one hour. It is equivalent to 3600 
watt-seconds or 60 watt-minutes. 

Watt-hours = watts X hours. 
The dials of consumer's meters, used to measure the elec- 
trical energy supplied for lighting and power, generally record 
watt-hours, ^[ 275. A kilowatt-hour is a larger unit of electrical 
work and is equal to 1000 watts or 1 K. W. expended in one 
hour, or 500 watts expended in two hours, etc. 

Kilowatt-Hours = K. W. x Hours. 



ELECTRICAL WORK AXD POWER. 219 

An electrical hnrse-power-hour is one electrical horse power 
maintained for one hour, or 746 watts maintained for one 
hour. 

Horse-power-hours = H. P. X hours. 

Electrical energy is generally supplied from stations at a 
fixed rate per horse-power-hour or kilowatt-hour. The total 
cost of producing a kilowatt-hour varies with many station 
conditions ; from about 2 to 7 cents per kilowatt-hour is the 
range in a number of plants. 

224. Electrical Power Calculations. — The following 
rules and formulae have been derived either by trans- 
posing the formulae in ^|^[ 220 to 224, or by combining 
them with the formulae given in Lesson XIII, Ohm's Law. 
This lesson is practically a continuation of Ohm's Law and 
is very important, as by it many practical electrical problems 
are solved. The formulae apply equally well to the whole or 
any part of a circuit ; as, for example, to the lead wires to a 
lamp, as well as to the lamp itself, or the internal resistance 
of a battery or dynamo. Caution must be exercised to use the 
volts lost or drop, ^[ 230, in the particular part of any circuit 
considered, also the resistance of, and the current through this part 
only. The symbols used to represent the quantities are as 
given heretofore, and are again enumerated as follows: 

E = pressure, E. M. F. or difference of potential, causing 
the current to flow, expressed in volts ; 

R = resistance of the circuit or part of the circuit ex- 
pressed in ohms ; 

C = current in amperes ; 

W= watts expended or lost in the resistance ; 
H. P. = electrical horse power (746 watts) ; 
K.W.= kilowatt (1000- watts). 

Case 1. — Given Current and Pressure to Find Watts 
Lost or Expended: 

TJie watts expended in any circuit equals the product of the cur- 
rent and the pressure causing it to flow, Formula (62). 

W=E X C. 

Prob. 82. — Find the energy expended in a lamp requiring 110 volts 
and ^ ampere. 

By Formula (62)) W = E X C = 110 X * = 55 watts. 



220 PRACTICAL ELECTRICITY. 

Case 2. — Given Current and Resistance, to Find the 
Energy Expended in Watts: 

The ivatts. lost or expended in emy circuit are equal to the cur- 
rent squared multiplied by the resistance. This is often called the 
C- square R loss. 

W = C 2 XR (68). 

This formula is obtained by substituting the value of 
E = C X R in Formula (62) W = E X C, which gives W = 
C X R X C = C 2 R. 

Prob. 83: The resistance of the field magnets of a dynamo is 220 
ohms and the magnetising current, 2 amperes. What energy is 
expended ? 

By Formula (68) W = C 2 R .= 2 X 2 X 220 == 880 watts. 

R = 220 ohms, C =2 amperes. 

Case 3. — Given Resistance and Pressure, to Find the 
Watts Expended : 

The watts lost or expended in any circuit are equal to the square 
of the pressure divided by the resistance. 

TTI2 

W = ^ (69). 

This formula is obtained by substituting the value of 

c = 5 in Formula (62) W = E X C, then W = E X £=5- 
R K K 

Prob. 84 : The hot resistance of a 110-volt incandescent lamp is 220 
ohms. What energy is expended in the lamp every second it burns? 

E 2 110 X 110 

By Formula ( 69 ) W = ^ = g20 — = 55 watt9 ' 

E = 110 volts, R = 220 ohms. 
Compare this result with Prob. 82. 

C ase 4, — Given Watts Expended and Current, to Find 
the Resistance : 

The resistance is equal to watts expended divided by the square 
of the current. 

R = 5, (70). 

This formula is found by transposing Formula (68). 

Prob. 85 : A 55- watt incandescent lamp requires \ ampere. What 
is its resistance? 



ELECTRICAL WORK AND POWER. 221 

W 55 55 

By Formula (70) R = ^ 2 = -^-= = -^ = 220 ohms. 

W = 55 watts, C = i ampere. 
Compare this answer with Probs. 82 and 83. 

Case 5. — Given Watts Expended and Resistance, to 
Find the Current : 

The current equals the square root of the ivatts divided by the 
resistance. 

c =^f (">• 

This formula is obtained by transposing Formula (68). 

Prob. 86 : If the hot resistance of a 55-watt lamp is 220 ohms, what 
current will it require ? 

By Formula (71) C = ^ = ^J| = ^\ = \ am P ere ' 
W = 55 watts, Fv — 220 ohms. Compare with Probs. 82, 84, and 85. 

Case 6. — Given Watts Expended and Pressure, to Find 
Resistance : 

The resistance equals the square of the pressure divided by the 
watts expended. 

*=w (72) - 

This formula is obtained by transposing Formula (69). 

Prob. 87 : What is the resistance of a 55 watt, 110 volt incandescent 
lamp? 

By Formula (72) R = ^ = 110 ^ 110 = 220 ohms. 

E = 110 volts, W = 55 watts. 

Case 7. — Given Watts Expended and Resistance, to 
Find the Pressure : 

The pressure is equal to the square root of the product of ivatts 
and resistance. 



E = /WXR (73). 

Prob. 88 : What pressure must be applied to an incandescent lamp 
of 220 ohms hot resistance so that it will receive 55 watts ? 

By Formula (73) E = */ W X li =/ 55. X 220 = 110 volts. 
W_55 watts, R = 220 ohms. 



222 



PRACTICAL ELECTRICITY. 



225. Electrical Power Formulae.— 

The above cases are summarized as follows : 
W = ExC Formula (62). 



W = C 2 X R 

E 2 



W 



E = 



E= /W X R 

E-CxR • 



= 


~ R 




W 


<J = 


~ E 


c = 


V 




E 


K 


~ C 




E 2 


Ii 


~W 




w 


K 


- p 2 



(68). 
(69). 

(64). 

(73). 
(29). 

(28). 
(63). 
(71). 

(30). 

(72). 
(70). 



If it is desired to use the larger unit of power, the horse power, 
the above formulae may be changed by remembering that 1 horse 
power = 746 watts, and they will then be as follows : 



EXC 
746 * 
C 2 XR 



746 



R 



E 2 



746~ 746 X R 
H. P. X 746 



From Formula (65) H. P. 
From Formula (68) H. P. 

From Formula (69) H. P. 

From Formula (65) E 

From Formula (65) C 

From Formula (75) R 

E X C 
From Formula (66) K. W. = -Jqqq-- 

C 2 x R 
From Formula (68) K. W. = iooo - 

E 2 
From Form ul a ( 69 ) K . W . = iqqq x R 



H. P. X 746 
E 
E 2 



H. P. X 746 



(65). 
(74). 

(75). 

(76). 

(77). 
(78). 

(66). 

(79). 
(80). 



ELECTRICAL WORK AND POWER. 223 

226. Power from Cells. — The amount of power that can 

be furnished by a cell is directly proportional to the square of 

its E. M. F. divided by its internal resistance and is equal to 

the number of watts expended by the cell on short circuit. 

Let W represent the power in watts from a single cell, then 

from Formula (72) we get 

E 2 
W=y (81). 

The power obtained from any number of similar cells is 
equal to the power of one cell multiplied by that number, 
and is independent of the grouping, provided that it is sym- 
metrical. For example, the amount of power a Leclanche 
cell can furnish if the E. M. F. is 1.5 volts and internal re- 

OK , E 2 1.5 X 1.5 _ ^ 

sistance .25 ohm= — = ^e — = " watts. 

The power furnished by ten cells would be 10 X 9 == 90 
watts. If arranged all in series then the total E. M. F. = 
15 volts and total internal resistance = 2.5 ohms, Formulae 

F 2 1 ^ v 1 ^ 

(36) and (37), and W = — = ^— ~^- = 90 watts. 

If arranged all in parallel then the total E. M. F. = 1.5 volts 
and the internal resistance = .025, Formulae (37) and (38), 

E 2 15x15 
and W = ~— Q05 == 90 watts as before, also 2 cells 

in series and 5 groups in parallel equal 90 watts as before, etc. 
In the above cases all the energy is expended inside the cell. 
For a steady current of maximum value through the external 
circuit, its resistance should be equal to the internal resistance 
of the battery. This is also the condition for a maximum 
rate of working or activity. The maximum economy for in- 
stalling a number of cells required for any given rate of work- 
ing is attained when the work is performed satisfactorily by 
the minimum number of cells. This condition is obtained 
when the total power the cells can maintain on short circuit 
is equal to four times the power required from them for the 
external circuit. 

To find the number of cells required for maximum economy 
of installation for any power to be developed: Multiply the 
power in watts required by the internal resistance of one cell and 
divide the product by the square of the E. M. F. of one cell. 



224 



PRACTICAL ELECTRICITY. 



Let N = number of cells required ; 

W = watts required in external circuit ; 
r = internal resistance of one cell ; 
E — E. M. F. of one cell. 



N = 



4X WXr 



E 2 



(82). 



Prob. 89 : How many chromic acid cells will be required for 
maximum economy of first installation to light a 12-watt incan- 
descent lamp? Each cell has an E. M. F. of 2 volts and an internal 
resistance of .5 ohm. 

T3 v i roo\ at 4XWXr = 4Xl2x.5 . 

By Formula (82) N= ^2 — — 0^0 = 6 cells. 



W 



E 2 2X2 

12 watts, E = 2 volts, r = .5 ohm. 



The cells in Prob. 89 could be arranged in any symmetri- 
cal combination to produce the 12 watts in the external cir- 
cuit. Suppose the 12- watt-lamp required 6 volts, then all the 
cells would be placed in series, Fig. 201. The E. M. F. of the 
battery would be 12 volts and the internal resistance 6 X .5== 
3 ohms, or the energy expended on short circuit by Formula 

E 12 X 12 
(81) W = -= — — =48 watts, or four times the energy 

required by the lamp. The resistance of the lamp is 
3 ohms, Formula (72), and when connected to the 6 cells in 
series will receive 2 amperes, Formula 

r6Voitr (37). The pressure sending the current 

rVT through the cells isCXr = 2x3 = 6 

volts, or one-half the E. M. F., and 6 volts 
are also maintained across the lamp termi- 
nals. The external power is thus 2x6 
= 12 watts and the watts lost in the cell 12 
watts, or the total watts = 24, or one-half 
the power the cells could deliver on short 
circuit. 

227. Efficiency of a Battery.— By 
efficiency is meant the relation of the useful 
work done to the total energy expended. 
A perfect battery, or dynamo (that is, one 
with no internal resistance), would deliver 
all of the energy to the external circuit, but 
as some portion of it is lost in the internal 
resistance the useful energy is always less than the total 
energy expended. If the total energy expended is represented 




r = 3p>* 

evoiu 



I* — evolt's "" 
pA/WVWWV-J 

C SLmparaa t tm I 



Li*. 



3 0T.r 

6VoJt 8 



Fig. 201.—' 
Lost" on the 
rial Resistance 



Volts 
Inter- 



ELECTRICAL WORK AND POWER. 225 

by 100, and one-half of this amount is unavailable for useful 
work, the efficiency would be 50 per centum or 50 per cent. 
In no machine, then, can the efficiency be 100 per cent. 

To Find the Efficiency of a Battery : 

Divide the resistance of the external circuit by the resistance of 
the external circuit plus the resistance of the battery. 

Eft =RT-r < 83 )- 

Prob. 90 : What is the efficiency of the battery in Prob. 89 ? The 
total resistance of the battery is 3 ohms and the resistance of the lamp 
is 3 ohms. 

By Formula (85) Eff. = ^-^ = ^~] = -50 or 50% . 

The total watts expended in ^| 226 are 24, and the useful 
watts in the lamp 12, so that the efficiency is the ratio of 

Useful watts 12 = _ 5Q = ^ ag before _ 



Total watts expended 24 

Let W = useful energy expended (in watts) ; 
w = useless energy expended (in watts). 

w 

Then, Eff.=^- (84). 

QUESTIONS. 

1. What is the difference between force and work ? 

2. Define mass ; energy ; power ; weight. 

3. What is the unit of (a) mechanical power? (b) Of mechanical 
work? (c) Of electrical work ? (d) Of electrical power? 

4. Cite examples illustrating the conservation and correlation of 
energy. 

5. How would you ascertain, by experiments, the mechanical 
equivalent of work performed by an electric current ? 

6. What is the difference between a kilowatt and a kilowatt-hour ? 

7. A battery used in electroplating has an efficiency of 70 per cent. 
What do you understand by this statement? 

PROBLEMS. 

1. How much electrical energy is expended in maintaining a 16 
candle power incandescent lamp, supposing that it has a resistance 
of 220 ohms (hot) and is taking 0.5 ampere ? How many watts per 
candle power ? How many such lamps can be maintained at full 
candle power by one mechanical horse power ? Ans. 55 watts ; 3.43 
watts ; 13 lamps. 
15 



226 PRACTICAL ELECTRICITY. 

2. A number of 100-volt incandescent lamps are being lighted by 
a dynamo generating 112 volts at the brushes. The resistance of the 
leads carrying current to the lamps is .05 ohm. Each lamp requires 
50 watts. How many lamps are burning? Ans. 480 lamps. 

3. {a) What size of generator (kilowatt capacity) should be pur- 
chased for a 500 light installation, supposing that standard 55 watt, 16 
candle power incandescent lamps are to be adopted? (b) What 
would be the K. W. capacity of a motor required to be substituted for 
a 25 horse power gas engine. Ans. (a) 27. 5 K. W. ; (b) 18.65 K.W. 

4. In constructing a solenoid and core to actuate a lever, 500 feet of 
number 18 B. & S., D. C. C. magnet wire were wound upon a brass 
spool. A table of heating limits gives 2 amperes as a safe carrying 
capacity for this size of wire under these conditions. Using this cur- 
rent, how much extra resistance must be added to place the coil across 
a line of 110 volts potential difference? Ans. 51.68 ohms. 

5. The above solenoid is to operate in series with the field magnets 
of a dynamo having 30 ohms resistance, (a) How much extra re- 
sistance must now be added to place the fields and coil in series across 
the above mains so as to receive the same current? (6) How many 
feet of No. 18 B. & S. iron wire are required to construct a rheostat for 
the extra resistance in this problem ? (c) If the average length of 
each turn on the solenoid is 4 inches, what is the magnetising force ? 
(d) How much energy is consumed in the solenoid? Ans. (a) 21.68 
ohms ; (6) 555 feet ; (c) 3000 A. T. ; (d) 13.28 watts. 

6. A street car is driven by two four-pole series motors. Each 
field magnet has a resistance of .125 ohm, the armature .125 ohm and 
an extra rheostat (diverter) has a resistance of 4 ohms. E. M. F. be- 
tween trolley wire and rails is 500 volts. Neglecting the counter E. 
M. F. of the motors, find the current the motors will receive in the 
following positions of the controller switch : (a) First point : Both 
motors in series, all field coils in series, extra resistance in series. 
(b) Fourth point : Both series motors in parallel and the extra re- 
sistance in series with them, (c) What power is the car receiving on 
the fourth point ? (d) Make a sketch of both controller combina- 
tions. Ans. (a)_ 95.238 amperes; (b) 115.942 amperes ; (c) 77.7 H. P. 

7. An electric automobile is equipped with 40 storage batteries 
which are connected, through the controller switch, for the first 
speed, 20 cells in series and two groups in parallel. Each cell has an 
E. M. F. of 2 volts and an internal resistance of 0.1 ohm. The re- 
sistance of the motors, extra resistance and leads at this combination 
is 0.5 ohm. (a) What is the value of the current required to start 
the vehicle? (b) How much energv is expended at the start? Ans. 
(a) 26.6 amperes ; (b) 1064 watts. 

8. While visiting an electric light station you note the following 
indications of instruments on the switchboard : voltmeter 115, am- 
meter 330. The plant operates the two-wire direct current system 
and uses 55-watt, 110-volt incandescent lamps, (a) How many lamps, 
at the instant of reading, are burning? (b) What is the load on the 
generator expressed in kilowatts and electrical horse power ? Ans. 
{a) 660 lamps ; (6) 37.95 K. W. ; 50.87 H. P. 

9 A compound wound dynamo is connected to a circuit to which 
the following apparatus is wired : 150 incandescent lamps, each re- 



ELECTRICAL WORK AND POWER. 227 

quiring .6 ampere ; 3 arc lamps, 10 amperes each ; various electrical 
cooking and heating appliances requiring when all are at work 20.5 
amperes ; two electroplating and electrotyping baths arranged in 
series across the mains and taking a maximum current of 5 amperes ; 
10 storage batteries in series with a lamp bank resistance across the 
mains and requiring a charging current of 10 amperes. The two-wire 
direct current system is used and a constant potential difference of 
110 volts is maintained between mains. What is the output of the 
generator in electrical horse power, supposing that the maximum cur- 
rent ever required is 75 per cent, of that taken when the whole in- 
stallation is at work? Ans. 17.19 H. P. 

10. Two arc lamps of 2000 and 1200 C. P., having a hot resistance of 
6 and 3 ohms respectively, and an incandescent lamp with 18 ohms 
resistance, are all placed in parallel across a pair of mains. An am- 
meter in the main circuit indicates 20 amperes, (a) What current is 
each lamp receiving? (b) What is the difference of potential between 
the mains? (c) What is the power absorbed by each lamp? (d) 
How many candles per watt in the 2000 C. P. lamp? Ans. (a) 12, 6, 2 
amperes ; (6) 36 volts, P. D. ; (c) 432, 216, 72 watts ; (d) 4.6 C. P. 

11. The mean effective steam pressure from an indicator card is 50 
pounds ; the speed of the engine, 290 revolutions ; length of stroke 10 
inches ; area of piston head 0.75 square foot. What horse power is de- 
veloped by the engine? Ans. 75.927 H. P. 

12. How many watts are expended in an arc lamp having a hot re- 
sistance of 4.5 ohms and requiring 50 volts ? Ans. 555 watts. 

13. What is the current flowing through an electromagnet having a 
resistance of 50 ohms and requiring 200 watts ? Ans. 2 amperes. 

14. What is the maximum power obtainable from aGrenet cell of 2 
volts, E. M. F. and an internal resistance of .02 ohm ? Ans. 200 watts. 

15. How many cells are required for maximum economy of installa- 
tion to operate an electromagnet requiring 20 watts? Each cell has an 
E. M. F. of 2 volts and an internal resistance of .5 ohm. Ans. 10 cells. 

16. If the magnet in question 14 has a resistance of 5 ohms and re- 
quires 10 volts, what is the best arrangement of the cells and what 
is the efficiency ? Ans. 80 %. 



LESSON XX. 

MEASUREMENT OF PRESSURE. 

Electromotive Force and Potential Difference— Hydraulic Analogy to 
Illustrate " Volts Lost " — Volts Lost in an Electric Circuit— Dis- 
tribution of Potential in a Circuit — Variation of Potential Differ- 
ence with Variation of External Resistance— Table XIV. Vari- 
ation of Current, Pressure and Resistance — Measurement of E. 
M. F. and P. D. — Construction of Voltmeters — Weston Voltmeter 
— Connecting Voltmeters — Measuring High Voltages w ith a Low 
Range Instrument —Measurements with a Voltmeter — Volts Lost 
in Wiring Leads— Comparison of E. M. F. of Cells by the Potenti- 
ometer — Questions and Problems. 

228. Electromotive Force and Potential Difference. — 

Volts lost or " Drop " in a Circuit. — Electromotive force is the 
total force generated, potential difference is any part of the 
total E. M. F., % 70. The E. M. F. of any generator is not 
available for use in the external circuit, since part of it is 
required to cause the current to flow through the internal 
resistance of the generator (battery or dynamo). By the 
expressions fall of potential, "drop" or " volts lost" in any 
part of a circuit is meant that portion of the E. M. F. which 
is used in causing the current to flow between the two points 
considered. For example, the " volts drop " across a lamp 
means the potential difference across the lamp terminals, it 
is the force which is causing the current to flow through the 
lamp. Two " volts lost on the line" means that this much 
pressure is lost or used in sending the current through the 
line. The E. M. F. is the sum of all the potential differences, 
as, the drop on the line plus the drop on the lamp plus the 
drop on the internal resistance of the generator. The term 
" volts lost " or " volts drop " implies that energy is lost, since 
energy is the product of volts and current, Formula (62); 
pressure could not be lost in any circuit unless a current had 
been transmitted by it. 

229. Hydraulic Analogy to Illustrate "Volts Lost." 

A hydraulic analogy may assist somewhat in understanding the 
fall of potential or volts drop in an electric circuit. In Fig. 202, T is a 
228 



MEASUREMENT OF PRESSURE. 229 

cylindrical tank filled with water under pressure due to the weight 
of the piston P, and AB is a pipe for transmitting the water to point 
B. With the valve at B closed" the pipe is full of water, but there is 
no current through it. The gauges at A and B, each indicate 60 
pounds per square inch', which represents the water-motive-force or 
power to move the water. When the valve is opened quarter-way 



B 



WeiaU of 



B 1* r 

ii p^j^ w (T) 6 g°4« 

^^T*wp«iD-i-iE2i J_ 



Difference it. Pressure 1011.9- 



Fig. 202.— Cylindrical Tank of Water and Trans- 
mission Pipe to Illustrate the Fall of Potential. JW«>t« 

r r>«ssur 

and a current of water is passed through the pipe, "Burk™ 
the pressure on the gauge at A is still 60 pounds, 
while at B it is only 50 pounds. The weight Wll 

of water is neglected. There is thus a difference in pressure 
of 10 pounds, between the two points A and B, and this force has 
been used or lost in overcoming the friction or resistance offered by 
the sides of the pipe to the running water. The available pressure 
at the B end of the pipe, which might be used for driving a turbine, 
is only 50 pounds, while the total pressure is 60 pounds. There is 
thus not a loss of quantity of water, but a loss of energy, as work has 
been performed in moving the water. Suppose the pipe to be of uni- 
form bore and 10 feet long, then a gauge inserted at a point one foot 
from A would indicate 59 pounds ; at two feet, 58 pounds, etc. ; or 
there is a gradual fall or drop of pressure along the pipe which is 
directly proportional to the length when the resistance is uniform, or 
a drop of one pound per foot in length. 

The difference in pressure between any two points is the pressure 
required to send the current between these points, and is found by 
subtracting the pressure of that gauge which is more distant from the 
generating source from the pressure of the gauge nearer to it. The 
valve is now opened half way and the gauge at A still indicates 60 
pounds, while that at B now indicates 40 pounds. A difference in 
pressure of 20 pounds is required to cause the increased current to 
flow through the pipe, leaving only 40 pounds available pressure to 
be applied to the turbine at B. A force of two pounds is required to 
send the increased current through each foot of the pipe, and the sum 
of the pressures lost in the 10 feet equals 20 pounds, or the difference 
in pressure between the points A and B. If the valve at B is opened 
still further the difference in pressure between A and B will be 
greater, since more water will flow, and the available pressure at B 
will be correspondingly less. If the transmitting pipe considered 
above is replaced by one much larger in diameter, the resistance will 



230 



PRACTICAL ELECTRICITY. 



be less; and less pressure therefore will be lost in transmitting the 
water, so that a greater available pressure will result. 

Suppose that the pipe AB is composed of several pieces of different 
sizes joined together, Fig. 203 ; with no current flowing the pressure 
at gauge B is equal to that at A. With the valve opened quarter way 
gauge A indicates 60 pounds and gauge B 50 pounds, as before, or a 
loss in pressure between the two points A and B of 10 pounds, which 
causes the current to flow between them. While the current of water 
may be the same as before and the total pressure lost also the same, 
the distribution of the lost pressure is not the same since the resist- 
ance of the pipe is not uniform, it being practically a number of pipes 
of different sizes, and therefore different resistances, connected in 
series. The greatest difference in pressure will be between points 
having the greatest resistance, such as the length of pipe of small 
diameter, where four pounds are required to send the current of water 
through this section of the pipe, while only two pounds are required 
to send the same current through the larger adjacent section. The 
opposition to be overcome in the pipe of smaller diameter is twice as 
great as in the larger pipe, since twice the pressure is required to 
send the same current through it. In hydraulics, calculations are 
made to deliver water at a certain rate of flow and under a certain 
pressure, in which case the pressure and energy lost in transmitting 
the water must be considered. The same is true in calculating the 
sizes of pipes for gas lighting, and of wires for carrying electric 
currents, f 239. 




A 

Weight of 



B 



IP is ton 
60lbsjoei-SCj. 
60lbs. 59lba 55lhs 

iffiffiKPCD 2) CD (D 



SO lbs 




Fig. 203.— Hydraulic Analogy of the Fall of Potential. 



230. Volts Lost in an Electric Circuit. — Consider now 
an electric circuit in which a generator (battery or clyamo) 
is supposed to maintain a constant pressure of 60 volts be- 
tween two parallel lines at the point A, Fig. 204, as indicated 
by a high resistance galvanometer or voltmeter. With 
no current flowing from the generator the voltmeter will 
indicate 60 volts at point B (neglecting the pressure used to 



MEASUREMENT OF PRESSURE. 231 

transmit the small current used by the voltmeter). By 
closing the switch at B one lamp is lighted, and an ammeter 
indicates 1 ampere flowing through the circuit. The volt- 
meter at A still indicates 60 volts, but the voltmeter at B 
only 50 volts. There is, therefore, a difference in pressure 
between points A and B of 10 volts, which is used in over- 
coming the resistance of the line and causing the one ampere 
to flow through it. The available pressure at point B to 
perform useful work in the lamp is, therefore, only 50 volts 
and causes one ampere to flow through it. There is no loss of 
current but a loss of energy on the line (10 X 1 = 10 watts) 
that is, work has been performed in transmitting the current 
from A to B just as in the case of the water. If 10 volts are 
required to send one ampere through the line, by Formula 
(30), its resistance will be 10 ohms. 

If the wire is of ^_^sv*it a 

uniform area and 10 
feet in length, from 
A to B, the volt- 
meter will indicate 
59 volts when placed + 
across the line at A 



^— gg ^© 




&. 



& 



Lan,p 
Switch 

B 



points 1-1, one foot — ^ |0Fcct I 

distant from A; 58 _,. ' ({TT ., _ ... _,. . . Z7^ . 

-i, , p , ; tig. 204. — Volts Drop" in an Electric Circuit. 

volts at 2 feet, or 

points 2-2, etc.; or the fall of potential along the line is 
directly proportional to its length and resistance. Since 
the total resistance of the line is 10 ohms the resistance of 
one wire is 5 ohms and the difference in potential required 
to send one ampere through 5 ohms isE = CxR = l X5 = 
5 volts. (Formula 29.) A voltmeter placed across one side 
of the line to include 10 feet of its length will indicate a po- 
tential difference of 5 volts drop or loss on this side, and the 
same drop on the other side of the line. Since there are 5 
volts drop on 10 feet of wire of uniform resistance the drop 
per foot will be \ volt, or 1 volt for every 2 feet, etc. The 
voltmeter when placed in parallel with any length of the wire 
will indicate the difference of potential between the points 
included. 

Now turn on the switch with a second lamp of such resist- 
ance that the ammeter indicates 2 amperes, Fig. 205. The 
voltmeter at A still indicates 60 volts as before, but that at B 



232 PRACTICAL ELECTRICITY. 

now indicates only 40 volts. The difference in pressure 
between points A and B is 20 volts, since twice the current 
through the same resistance requires double the pressure to 
be applied. The available pressure aj^plied to the lamps is 
40 volts. If the wires considered above were just double the 
area, only one-half of the pressure would be lost on the leads, 
and therefore one-half of the energy lost, and a higher avail- 
able P. D. at point B would be maintained. 

Suppose the transmitting line to be composed of several 
wires of different sizes connected in series as represented 

(v^) eov.it. ^ iovwu C7iX> «*i» ¥ th n e heavy and 

V_4/ s \t_-/ v \I_i/ thin lines in Fig. 




2^2 



■p-y-L . 206. With one 
2 1" 2 1* l am P connected 



at B, the volt- 

eiovoits' / * meter may read 
' 50 volts, as be- 



Fig. 205.—" Volts Drop" in an Electric Circuit. f ore ] )U ^ ^g f a ]j 

of potential or drop on the line, 10 volts, will not now be uni- 
form , since the resistance is not uniform. The greatest potential 
difference or drop will be between the points of highest re- 
sistance. Consider the equal lengths of wire E F and F G 
of unequal areas. The current is the same through each, but 
the voltmeter indicates 3 volts when connected across points 
E F, and only 1 volt when placed across points F G. The 
thin wire E F has three times the resistance of the wire F G, 
since three times <^~n> s — s <^~n <^"*n 

n \ VM/60 Volts \VM/3Volts \VM/IVo» VVM/a 

the pressure is \L-aJ pAL_iA AL_sA— ^ 

required to send y W E f ^r 

xi + /-n \ \— 'Foot -4,-iE.ot _ 

the same current (d) ^->. ^^ 

through it. The ^ 1 \^j/ IA ' 



drop in volts in A c d B 

Other portions of * ig " 20t >-~" v °l ts Drop" in an Electric Circuit. 

the circuit may be measured in the same manner, the sum 
of all the readings being equal to the total loss on the line, 
or 10 volts. The watts lost in E F are also three times as 
great as in F G, or three watts and one watt respectively, 
Formula (62). The total watts generated at point A with one 
lamp in circuit = 60 X 1 = 60 watts. The watts lost on the line 
= 10 X 1 — 10 watts, thus 50 watts are expended in the 
lamp. By Formula (84) the efficiency of this part of the 
circuit will be 50 -*- 60 = .83£ = 83 J %. 



MEASUREMENT OF PRESSURE. 233 

231. Distribution of Potential in a Circuit. — In the 

above illustrations the pressure was assumed to be main- 
tained constant at point A. Consider now a battery or 
dynamo D, Fig. 207, with an internal resistance (r) of 4 ohms 
connected to one lamp at B, 10 feet distant from A. The 
voltmeter at A indicates 60 volts as before, and with one 
ampere flowing through the lamp, 50 volts at B. Ten volts 
are required to send one ampere through the lead wires, 
and since the internal resistance of the generator is 4 ohms, 
4 volts will be required to send one ampere through it, 




Fig. 207. — E. M. F. and Potential Difference in an Electric Circuit. 

Formula (29). The total pressure or E. M. F. is, therefore, 
4 -j- 10 + 50 or 64 volts. The voltmeter across the generator 
terminals, however, indicates the potential difference or that 
portion of the E. M. F. available in the external circuit, 60 
volts. If the lamp at B is turned out the voltmeters at both 
points A and B will indicate 64 volts, or the E. M. F. of the 
source of electricity. Now connect two lamps in circuit, 
Fig. 208; the resistance of one lamp is 50 ohms, and of 
two in par- . — ^ . — ^ 

all el it is 57-6 volt s. \VM/ W^^' 

25 ohms, ^i^fsT ^^ jr*4(S <S 
Formula r4_^AJ ^s. •*«* X X 
(43). The -^P-Sgy. iT-T 

TOTil 1 vpm^t- 

ance of the Fi S-208.— E. M. F. and Potential Difference in Electric Circuit. 

circuit, R -j- r = 10 -f- 25 -f- 4 == 39 ohms, and the current, 
therefore, equals 64-^39 or 1.64 amperes, Formula (28). 
The voltmeter at B indicates 1 .64 X 25 = 41 volts, Formula 
(29), while voltmeter at A indicates 1.64 X (10 -f 25) = 
57.4 volts potential difference at the generator terminals. 
The drop on the internal resistance is 4 X 1.64 = 6.56 
volts or total E. M. F. 6.56 + 57.4 = 64 volts (nearly). If 
the lamps require 50 volts to send sufficient current through 
them to give the proper amount- of light, with 40 volts across 



234 PRACTICAL ELECTRICITY. 

their terminals they will now burn dimly, since each lamp 
does not receive one ampere, as before. The total E. M. F. 
must be increased, say by adding more cells in series, or 
increasing the field strength of the dynamo, if 50 volts are to 
be maintained across the two lamps in parallel. If one lamp 
is then turned out the other lamp receives a greater pressure 
than 50 volts, since the drop on the leads and internal resistance 
is less when the current through them is diminished. The 
E. M. F. must therefore be decreased as the current is de- 
creased and increased when the current increases. In a 
battery installation for lighting lamps a special switch is 
designed to connect, or disconnect several end-cells as the 
voltage regulation may require. This switch is called an 
t tS<Sh u « 3 end-cell switch. In a dyna- 

mo the E. M. F. is varied 
» 4av by increasing or decreas- 
L ing the field strength of 
J the electromagnets. 

f45Wl45KT45V Prob. 91 : Eight arc lamps 
are connected in series to 
a series dynamo, Fig. 209, 
Fig. 209.-E. M. F and Potential Difference each lamp requires 45 volts 
in a Series Arc Light Circuit. and 1Q ampereg< The re _ 

sistance of the series field is 4.5 ohms and the armature has a resistance 
of 4.5 ohms, (a) What pressure will be indicated by a voltmeter 
placed across the brushes? (b) What is the E. M. F. of the gener- 
ator? (c) How much energy is lost in the internal and external 
circuits? (d) What is the electrical efficiency? See Fig. 209. 

By Formula (30) K = ?- = 45 = 4.5 ohms per lamp. 

' C 10 

Resistance of 8 lamps in series = 8 X 4.5 = 36 ohms. 

By Formula (29) E = C X R = 10 X 36 = 360 volts potential dif- 
ference (a). 

Total resistance, r + R = 4.5 + 4.5 + 36 = 45 ohms. 

By Formula (33) E. M. F. =C X (R + r) = 10 X 45 = 450 volts (b). 

By Formula (62) W = E X C =360 X 10 = 3600 watts external cir- 
cuit. 

By Formula ( 62) W = E X C = 450—360 = 90 volts X 10 = 900 watts 
internal circuit (c). 

By Formula (84). EH. = ^ = ^ m = .80 = 80 per 
cent. (d). 




Tip 

■6\ 



MEASUREMENT OF PRESSURE. 



235 



232. Variation of Potential Difference with Variation 
of External Resistance. — 

Exp. 64 : Connect a voltmeter to a Grenet cell and also a variable 
resistance, R, in series with an ammeter, Fig. 210. With switch, S, 
open, the voltmeter indicates 2 volts or the E. M. F. of the cell. 
Adjust arm A of the rheostat so that a very high resistance will be 
connected to the cell, sav 100 ohms, when switch, S, is closed. The 
voltmeter now indicates 1.999 volts or the potential difference is 
nearly equal to the E. M. F. when the external resistance is high, 
since very little current flows. Now reduce R 
to about 9.6 ohms ; if the cell's resistance = .4 

2 
ohm, r + R = 1 oh ms and the current =-t^ = 

.2 ampere. The voltmeter indicates C X R — 
.2 X 9.0 = 1.92 volts potential difference which 
is causing .2 ampere to flow through 9.6 ohms, 
the remaining .08 volt is required to send the 
same current through the internal resistance. 
Reduce the external R to .4 ohm and the volt- 
meter indicates 1 volt P. D. 
resistance is now equal to the internal resist- 
ance there is 1 volt drop inside the cell. Short circuit the cell by a 
very low resistance and the voltmeter indicates practically zero, the 
current from the cell is a maximum and all of the E. M. F., 2 volts, 
is used in sending the current through the cell's internal resistance. 
The preceding experiments may be summed up in the following 
table, which can be verified by the apparatus in Fig. 210 : 

Table XIV.— Variation of Current, Pressure, and Resistance. 




Fig. 210. — Variation of 
P. D. and Current with a 
Since the external Variation of Resistance. 



Ohms External Circuit, R. 


Volts Across Battery, P. D. 


Amperes, C. 


Infinity 


Equal to E. M. F. 

Verv little less than 

E. M. F. 





Great compared with r 


Small 


R, say any value 


R+ r XE.M.F. 


E. M. F. 
R + r 


Small compared with r 


Small 


Large 








Maximum and equal 

E. M. F. 

to r 



The following formulae derived from Ohm's Law will be 
found useful in calculating the internal resistance and po- 
tential difference : 

Let E — E. M. F. in volts ; 
P. D. = Potential difference (P. D.) in volts. 



236 PRACTICAL ELECTRICITY. 

C - -JT' 

C=^|^ (85). 

«_ E 



By combining the first and third equations we get, 

P. D. = E^ 
R R+r' 

orP.D. = |-^| (86). 

From Formula (85> r = E ~?' —' (87). 

By Formula (87) a cell's internal resistance may be measured by 
noting the voltmeter and ammeter readings when it is connected, as 
in Fig. 210. 

Prob. 92: The E. M. F. of a Leclanche cell is 1.4 volts; P. D., 
measured at the battery terminals when .8 ampere is flowing, is 1 
volt. What is the cell's internal resistance ? 

By Formula (87) r = g — P.D; = 1.4 — 1. = 1 ohm 

E = 1.4 volts, P. D. =1 volt, C = .8 ampere. 

Prob. 93 : The E. M. F. of a dynamo is 112 volts ; resistance of 
lamp circuit 5 ohms ; resistance of armature .05 ohm. What P. D. 
will a voltmeter indicate when placed across the brushes ? 

By Formula (86) P. D. =-|^? = 44^1 =1*0.8 volts. 
J v ' R -f r 5 + .0.') 

E = 112 volts, R = 5 ohms, r = .05 ohm. 

233. Measurement of E. M. F. and P. D.— Consider 
first the following hydraulic analogy in which it is desired to 
measure the true water pressure at the point C in a pipe, Fig. 
211, through which a current of water is flowing from point 
A to point B. Instead of using a spring gauge which con- 
sumes no water in making the measurement, we will use a 
turbine wheel at point C. A jet of water is therefore forced 
against the wheel, which revolves at a particular speed for a 
given pressure at point C, say, 1600 revolutions per minute, 
corresponding to a pressure of 50 pounds per square inch at 
C. Is this the accurate pressure at point C, or is it the pressure that 
would be recorded by a spring gauge if inserted at point C ? No. 
The turbine in measuring the pressure will increase the flow 
of water at point C, as some water must necessarily discharge 



MEASUREMENT OF PRESSURE. 237 

through it. The accurate pressure will not be recorded, but 
a lower pressure than that which exists when the turbine is 
not connected. The increased current of water through the 
pipe from A to C, due to the turbine outlet, causes a greater 
loss in pressure. If the turbine were made exceptionally 
small and sensitive so that a very minute stream of water 
from the outlet would actuate it, it would more nearly record 
the true pressure at point C, since very little more current 
would then flow c=^o than when it was disconnected. 

This turbine j- v pressure meter must therefore be 

constructed so ' ^ M that only a very small amount of 
water will be 

used by it in \\ c & 

measuring the « — _ ~ v \ ^ 



water pressure. VjTtiRfwvF 

To measure &tp 

the electrical _. „.. .. , _ _ ,"' ; .. _, 

top £ Fig. 211.— Measurement of Hydraulic Pressure. 

difference of 

potential between two points requires a galvanometer con- 
structed with a very high resistance, so that only a very mi- 
nute current will flow through it, at the same time the current 
must be of sufficient strength to actuate the movable system, 
which is generally quite sensitive, •[[ 180. To measure electri- 
cal -pressure some current must therefore be used, and the true press- 
ure will be greater than the indicated pressure by an amount equal 
to the volts lost on the line and generator which are required to 
transmit the voltmeter current to the instrument. The less this 
current the more accurate the indication, consequently the best 
voltmeters have a very high resistance and their current is prac- 
tically negligible. When a voltmeter is placed in parallel 
with any part of a circuit the resistance of the circuit is 
practically the same as before, since the voltmeter resistance 
is so very high the current in the circuit is not materially 
changed, and the calibrated indication records, not the current 
in the circuit, or the current through the voltmeter, but the 
difference in pressure between the voltmeter terminals. The 
movement of its magnetic system, of course, depends upon 
the current flowing through the voltmeter, but the scale is 
calibrated by applying known E. M. F.'s to its terminals and 
marking the position of the needle with reference to the scale 
for each particular pressure applied, H 180. In an ammeter 
the whole current passes through the instrument, or its 



238 



PRACTICAL ELECTRICITY. 




shunt, and the instrument measures the current. A voltmeter 
measures the current flowing through it, but the calibration is 
in terms of the pressure causing this current to flow. See Exp. 

57,1[182. 

234. Construction of Voltmeters.— The same principles 
employed in the construction of ammeters, 1[ 204, etc., are 

employed in construct- 
ing voltmeters, the only 
difference being that the 
windings are of very fine 
wire, suitable to the 
small current that is to 
be carried, and that ex- 
tra resistance coils are 
generally added in series 
with the voltmeter coils 
to produce an instru- 
ment of very high re- 

^.2i2.-Weston . sistance, for the reasons 

already given. lhe 
method of calibration is given in H 182. 

235. Weston Voltmeter. — The same construction is em- 
ployed in this make of voltmeter as in the Weston ammeter, 
11 208, extra resistance being connected in series with the 
movable coil and the terminals brought out to binding posts, 
Fig. 213. A double- scale Weston voltmeter is shown in Fig. 
212, suitable for use with pressures as 
high as 150 volts. The 150 volt coil 
terminates in the lower right and 
left-hand binding posts, and the cur- 
rent enters by the right-hand post 
marked -{— A push-button above 
this post serves to close the circuit. 
The resistance of the 150 volt coil 
is about 150,000 ohms, and there 

are 150 divisions 011 the Upper, or Fig. 213. — Connections of 
black ink scale, or one division per Weston Double Scale Volt- 
volt. The 15 volt coil terminates in 

the lower right-hand and upper left-hand posts, and has a 
resistance of about 1500 ohms. There are ten divisions on 
this red ink scale per volt, so that one-tenth, five-hundredths 




MEASUREMENT OF PRESSURE. 



239 



or even twenty-five thousandths of a volt may easily be read 
from this scale. In using a double scale voltmeter, if in 
doubt about the value of the voltage to be measured, always use 
the higher reading scale first, then if the value is below the 
limit of the low reading scale, the left-hand terminal may 
be readily changed to the upper post marked 15. If 150 volts 
are directly applied to the low reading scale the instrument 
will be seriously damaged and probably the insulation de- 
stroyed by a larger current flowing through it than the wind- 
ings will carry. This wire may be as small as .001 inch in 
diameter. For the same reason any voltmeter should not be 
subjected to a higher voltage than is indicated upon its 
scale. Voltmeters are calibrated by means of standard cells 
and are made up according to the range of the instrument 
desired, by means of the extra resistance to be added. In a 
milli-voltmeter the scale is graduated to read in divisions, 
representing one-thousandth part of a volt, or one millivolt 
With a good voltmeter many practical electrical measure- 
ments may be made, some of which are given in the Appen- 
dix. 

Prob. 94 : A 150 volt coil of a Weston voltmeter has a resistance of 
150000 ohms. What current will it receive when placed across a cir- 
cuit of 100 volts P. D. ? 



By Formula ( 28 ) C = £ = 



100 



150000 
E = 100 volts, R 



= .00066 ampere. 
150000 ohms. 



236. Connecting Voltmeters. — Voltmeters are connected 
directly across the line, the P. D. of which is required, or in 
parallel with 
the conduc- 
tor between 
the ends of 
which the 
voltage is re- 
quired. Figs. 
204, 205, etc, 




Fig. 214. — Connections of a Volt and Ammeter to a Circuit. 



illustrate the proper connection for measuring 
the potential in the different parts of a circuit. A voltmeter 
is never connected in series with the line and an ammeter never 
across or in 'parallel with the line, but always in series with 
it, see Fig. 214. The following problems will illustrate the 
reason for each particular connection. 



240 



PRACTICAL ELECTRICITY. 



Prob. 95 : In Fig. 214 the dynamo, D, maintains 110 volts across 
the mains at the lamps when 22 lamps are connected. Each lamp 
has a resistance of 220 ohms. What current will be indicated by the 
ammeter ? 

By Formula (43) J. K.= ?L = ??? = 10 ohms, 
nq 22 

110 



By Formula (28; 






10 



= 11 amperes. 



Prob. 96 : Suppose the voltmeter, in Prob. 95, has a resistance of 
110000 ohms and is incorrectly placed in series with the lamps. 
What current will the lamps receive, assuming the potential to be 
110 volts ? 

By Formula (28) C= | = 11(K ^° +10 = .0009 ampere. 

The lamps will not illuminate with this current since 10 amperes 
were required before. 

Prob. 97 : Suppose the above ammeter has a resistance of .1 ohm and 
is incorrectly connected across the circuit, like the voltmeter in Fig. 
214, what current will it receive if the P. I). is 110 volts? 

By Formula (28) C = J| = 115 = 1100 amperes. 
K .1 

Unless the ammeter had a current carrying capacity of 1100 amperes 
it would be destroyed by the excessive heat caused by such a large 
current. 

237. Measuring High Voltages with a Low Range In- 
strument. — Suppose it is desired to measure the potential dif- 
ference between a trolley line and the track which is about 550 
volts, and only a 150 volt instrument is available. Connect 

five 110- volt lamps in series 
and to the track and line, and 
parallel the voltmeter with 
each lamp respectively. The 
sum of the voltages across 
each lamp equals the P. D. 
between the line and the track. 
In a similar manner other 
high voltages may be ascer- 
tained. 

238. Measurements with 
a Voltmeter. — 







30 VOLTS 



Fig. 215 - 
Drop 



-Measuring the "Volts 
with a Voltmeter. 



Exp. 65 : Four spools of wire 
A, B, C, and D, Fig. 215, with 
resistances of 2, 3, 4, and 6 ohms respectively, are connected in ser- 
ies and to a battery. The spools may represent lamps, magnets, or 



MEASUREMENT OE PRESSURE. 



241 



e VOLTS DROP 




Fig. 216.— E 



and Potential 



any other electrical devices. When the battery circuit is closed 
through the above circuit, and the voltmeter connected directly 
across its terminals, 30 volts potential difference is indicated. The 
total external resistance is 2 -f- 3 -4- 4 -4- 6 = 15 ohms, and the 30 
volts potential difference indicated by the voltmeter is the pressure 
causing the current to flow through this external resistance. The 
current is, by Formula (28) 30 -=- 15 = 2 amperes. 

To measure the proportion of the total P. D. , 30 volts, causing the cur- 
rent to pass through the 2 ohm spool, A, Fig. 215, the voltmeter is 
placed in parallel with it, or connected to the points H and K, and in- 
dicates 4 volts. When the ^ volts drop 
voltmeter is connected across .,, . 
the 3 ohm spool B, 6 volts are M r-dXJMXJv^- 
indicated. The current is the 
same as through spool A, the 
resistance, however, being 
H times as great as A re- 
quires, also 1J- times the 
voltage that A requires. 
Spool C has 4 ohms, or twice 
the resistance of A and the 
voltmeter indicates 8 volts. 

By Formula (29) the volt- 
age required to send 2 am- 
peres through 4 ohms is cal- 
culated to be 8 volts, also in spool A the calculated voltage is 
E = C X R = 2 X 2 = 4 volts. The results of the measurements 
across the four spools by a voltmeter are indicated in Fig. 216, 
the sum of the volts drop on all the spools is 4 -4- 6 + 8 + 12 = 30 
volts or the potential difference measured at the battery. The total 
external resistance is 15 ohms, the current 2 amperes, and by Formula 
(29) the potential difference equals C X R = 15 X 2 = 30 volts. Sup- 
pose the internal resistance of 
the cells, r, is 5 ohms, then E = 
CXr or 2 X 5 = 10 volts drop 
in the cells. If the voltmeter is 
connected across the battery it 
indicates the P. D. 30 volts, 
when 2 amperes are flowing. 
If the external circuit is now 
opened the voltmeter indicates 
the E. M. F of the cells, which 
is the sum of all the former 
potential differences in the cir- 
cuit or 30 + 10 = 40 volts 
E. M. F. or the indication of 
the voltmeter now. 
a fine German silver wire, AB, uniform in 



Difference in a Circuit. 




YM 



Fig. 217.— Fall of Potential Along 
a Wire. 



Exp. 66— In Fig. 217, 
size, is stretched on a board between binding posts and a scale of 
inches arranged directly above it. The wire is connected in circuit 
with one or more cells, preferably of the Daniell type, so that the cur- 
rent flowing through the wire will be constant. If the terminals of a 
16 



242 



PRACTICAL ELECTRICITY, 



galvanometer or voltmeter are held on the wire, so as to include a 
portion of its length between them, as in Figure 217, the potential 
difference between the points embraced will be represented by the 
value of the deflection. One terminal may be fixed stationary at point 
A and the other terminal gradually moved along the wire toward B. 
The deflection increases as you proceed toward B. For example, with 
six inches between voltmeter terminals the drop is .4 volt ; 12 inches, 
.8 volt, etc. 

Since the current is the same in all parts of the circuit the 
same deflection will be produced for equal distances on the 
wire, provided its resistance is uniform. If a copper wire of 
the same size is connected in series with the German silver, 
the volts drop on 12 inches of copper will about equal the 
drop on 1 inch of German silver, since the latter has about 
twelve times the resistance of copper, and to send the same 
current through it, therefore, requires twelve times the pres- 
sure. The student should make a comparative table of 
lengths and deflections for several different wires of the same 
size joined in series, as the following : 



Inches. 


Copper 


German Silver 


Iron 


Deflections. 


Deflections. 


Deflections. 


5 . . . . 

10 ... . 
15 ... . 
Etc. . . . 










JVQLT LOST 



iO 



239. Volts Lost in Wiring Leads.— The size of wire re- 
quired to conduct a given current a certain distance may be 

readily obtain- 
ed by finding 
its resistance 
jr by Ohm's Law. 
In Fig. 218 a 
dynamo, D, is 
supplying cur- 
rent, 20 am- 
peres, to a num- 
ber of lamps, 
The potential at meter 
There are thus 2 volts 



1 



no VOLTS 



1 VOL.7 LOST- 



Fig. 218.— "Volts Lost" in Wiring Leads. 



L, located at a distance of 100 feet, 
is 112 volts and at lamps 110 volts. 
dropped on the line, or two volts are required to send 20 



MEASUREMENT OF PRESSURE. 243 

amperes through the 200 feet of copper wire. By Formula 
(30) the resistance of .the line equals E-^C = 2-^-20 = 
.1 ohm per 200 feet, or .5 ohm per 1000 feet. From the 
wire table, on p. 113, is found the nearest size of wire cor- 
responding to .5 ohm per 1000 feet, which is a No. 7. 

As a check upon this calculation the table of carrying 
capacities, % 257, should be consulted to further ascertain 
whether the wire is large enough. 

240. Comparison of E. M. F. of Cells by the Potenti- 
ometer. — The potentiometer is a simple instrument for 
measuring potential differences, or the E. M. F. of a cell. It 
consists of a fine German silver wire, AB, stretched between 
binding posts on a wooden base provided with a scale, Fig. 
219. Current is passed through this wire in one direction, 
A to B, from several constant current cells, so that there is a 
constant P. D. between the ends of the wire, AB. 

If this potential difference is known, the cell, the E. M. F. 
of which is to be determined, is connected in series with a 
galvanometer, and then in shunt with the potentiometer wire, 
so that its current will be in opposition to the potentiometer 
current. When the drop on the length of the potentiometer 
wire is equal and opposite to the cell' s E. M. F. no current 
will flow through the galvanometer, and its needle will stand 
at the zero position. This point is determined by sliding the 
movable contact, C, along AB, till balance of the needle is 
obtained at zero. Then the E. M. F. of the cell bears the same 
relation to the P. D. between the ends of the potentiometer 
wire, AB, as the distance included between the cell terminals, 
AC, bears to the whole length of 
the potentiometer wire, AB. p ±=SL± 'l | l , l , r = - 

The potentiometer wire scale 
may be graduated to read in 
volts instead of inches. Thus 
36 inches with 3 volts P. D. 
maintained would be 12 inches Fi s- 2i9.-Connections of Potenti- 
per volt. If the E. M. F. of 

one cell is known and used as a standard of E. M. F. the 
E. M. F. of any other cell may be determined from this 
standard. 

The standard cell is first connected to the potentiometer 
wire, Fig. 219, and the distance, AC, on the scale divisions 
noted when balance is attained, The cell of unknown 




244 PRACTICAL ELECTRICITY. 

E. M. F. is then substituted for the standard, being con- 
nected in opposition as before, and the distance AD noted 
when balance is obtained. 

The following relation then exists when AC equals length 
on potentiometer wire balanced by the standard cell, and AD 
equals length balanced by the unknown cell : 

E. M. F. Standard _ Length AC 

E. M. F. Unknown ~~ Length AT)' 

^ _ ., „ E. M. F. Standard X AD rQQ . 
Or unknown E. M. F. — j^ (88). 

When the potentiometer wire is graduated in volts, a 
voltmeter may be readily calibrated or re-calibrated, by sub- 
stituting it for the cell and galvanometer, and noting the de- 
flections on the voltmeter scale due to different potential 
differences applied by moving the flexible slider along the 
potentiometer wire. 

Prob. 98 : In a potentiometer test the standard cell, 1.05 volts 
E. M. F., produced a balance when 12 inches of the potentiometer 
wire were included between its terminals. What is the E. M. F. of 
two other cells measured if the potentiometer readings to produce 
balance were respectively 8 and 20 inches ? 

By Formula (88) Unknown E. M. F. = 
E. M. F. Standard X Length AD = 1.05 X 8 M 

Length AC 12 

first cell. 

E. M. F. of Standard cell = 1.05 volts, AD = 8 inches, AC = 12 
inches. 

Also 1-05 X 20 = L?5 voltgj E M F of the gecond cell# 



QUESTIONS. 

1. The E. M. F. of a cell measured by a voltmeter is 1 .8 volts. When 
connected to a spool of wire the voltmeter across the battery termin- 
als indicates only .7 volt. Account for the volts lost, and state 
what pressure is applied to the spool. 

2. Four coils of wire having resistances of 1000, 100, 10 and 1 ohms 
respectively are successively connected to a battery of 10 volts E. M. F. 
What will be the comparative value of the readings of a voltmeter 
placed across the terminals as compared with the E. M. F. ? State 
also the comparative current strength in each case. 

3. It is desired to measure the P. D. across a 250-volt power cir- 
cuit, and only a voltmeter with a 100-volt scale is at hand. How would 
you make the measurement using this instrument? 



MEASUREMENT OF PRESSURE. 245 

4. The greater the current flowing through a voltmeter or amme- 
ter the greater the deflection of its magnetic system. How then 
does a voltmeter measure electrical pressure ? 

5. In a potentiometer test balance of the galvanometer needle is 
attained with a standard cell of 1.05 volts for 210 divisions. For an- 
other cell the balance is attained at 430 divisions. What is the 
E. M. F. of the unknown cell? Give complete sketch. 

6. What is the essential requirement in order to measure E. M. F. 
accurately, and how is it f ultilled in voltmeter construction ? 

7. Since the mechanical construction and resistance of the movable 
coil of a Weston voltmeter and ammeter are both the same, what 
then is the essential difference in the instruments ? 

8. Make a sketch of the internal connections of a Weston volt- 
meter. 

9. What is a potentiometer, and for what is it used? 

PROBLEMS. 

1. Find the size of wire required to conduct current to 100 55-watt 
lamps in parallel, located at a distance of 125 feet from the dynamo, 
which maintains a constant pressure of 112 volts at its terminals. 
The lamps receive 110 volts. Ans. No. 2 B. & S. 

2. What power is lost in the leads in question 1 ? Ans. 100 watts. 

3. What P. D. must be maintained at the terminals of a dynamo 
so that 150 lamps, in parallel, each requiring 55 watts at 110 volts, 
will receive their proper current? Resistance of leads .02 ohm. 
Ans. 111.5 volts. 

4. If the internal resistance of the armature in problem 3 is 
.05 ohm, what E. M. F. is developed by the machine? Ans. 115.25 
volts. 

5. How much resistance must be inserted in series with two 50- 
volt 50- watt lamps, to allow them to be placed in series across a 220 
volt circuit? Ans. 120 ohms. 

6. We desire to run a motor, requiring 1 ampere, at 6 volts from an 
Edison circuit of 110 volts potential difference. If two 50-volt 50-ohm 
(hot) incandescent lamps are connected in series with the motor, how 
much additional resistance must be added to meet the requirements ? 
Ans. 4 ohms. 

7. One hundred incandescent lamps, 110 volts 55 watts each, are to 
be installed in a private house. The distance from the meter to the gen- 
eral centre of distribution on the second floor is 150 feet. Potential 
at the meter is 113 volts and at the point of distribution 111 volts. 
Calculate the size and weight of wire required, using the two-wire di- 
rect current system. Ans. No. IB. & S., 73.5 or 76 lbs. 

8. It is believed that the amount of power lost on a certain feeder 
in a central station is excessive. You are consulted and asked to de- 
termine the power so lost and the yearly cost of the same. The data 
furnished by the company is as follows : station runs 10 hours per 
day ; the cost of producing an electrical horse-power-hour is 3.5 cents ; 
the average daily load on this feeder is 100 amperes ; the size of wire 
is No. 2. B. & S. gauge, and the distance to the point of distribution is 
1000 feet ; the system used is two- wire direct current. Ans. $555.74. 



246 PRACTICAL ELECTRICITY. 

9. You are required to construct an electric heater for a trolley car, 
and find by experiment that 10 amperes flowing through a No. 16 B. 
& S. iron wire will radiate sufficient heat for the purpose. Assuming 
that the potential difference between trolley wire and track is 500 volts, 
find the length of wire required to properly place the stove in parallel 
with the circuit, (Neglect the rise in resistance due to the heat. ) Ans. 
2038 feet. 

10. The two field magnets of a bipolar dynamo have a resistance of 
55 ohms each, and are connected in series and placed in shunt with 
the brushes where 110 volts are maintained, (a) What is the field 
exciting current? {b) What is the total magnetising force, if the 
length of wire on each spool is 12,000 feet and the mean length of one 
turn 2 feet ? (c) What will be the exciting current when the fields are 
placed in parallel with the brushes ? Ans. (a) 1 ampere ; (b) 12,000 A. 
T. ; (c) 4 amperes. 

11. (a) How much resistance would you insert in circuit with a 50 
volt 50- watt incandescent lamp, to allow it to be properly placed across 
a 110-volt circuit? (6) How many feet of No. 18 B. &S. German silver 
wire are required to make a rheostat for this purpose? Ans. (a) 60 
ohms; (6) 759 feet. 

12. Four electromagnets having resistances of 4, 6, 8 and 10 ohms 
respectively, are connected in series and to a battery having an in- 
ternal resistance of 2 ohms. When the switch is closed a voltmeter, 
across the battery terminals, indicates 56 volts, (a) What will be the 
indications of a voltmeter when paralleled with each spool? (6) 
What will the voltmeter indicate when placed across the cells when 
the magnets are disconnected? (c) What will be the efficiency of 
the battery when connected to the circuit? Ans. (a) 8, 12, 16 and 20 
volts ; (6) 60 volts ; (c) 93 per cent. 

13. What will be the drop on 500 feet of No. wire used as an 
overhead trolley line at the instant when it is supplying current to 
four cars, each requiring 70 amperes? Ans. 14.2 volts.* 

* The student is advised to calculate resistances rather than take them from the wire 
table. Answers given for problems are based upon calculations from the formulae given 
in this book. 



LESSON XXI. 

MEASUREMENT OF RESISTANCE. 

Measurement of Resistance (Fall of Potential Method)— Measuring 
the Resistance of Arc and Incandescent Lamps While Burning — 
Measurement of Resistance (Substitution Method) — Drop Method 
of Comparison — Voltmeter Method — By Weston Instruments — 
Wheatstone Bridge (Principle of Slide Wire Pattern) — Lamp 
Chart Analogy of Wheatstone Bridge — Construction and Use of 
Slide Wire Bridge — Student's Wheatstone Bridge (Lozenge Pat- 
tern) — Operating the Bridge — To Measure a Higher Resistance 
Than That in the Rheostat— To Measure a Low Resistance — The 
Best Selection of Resistances for the Bridge Arms — Commercial 
Wheatstone Bridge — Direct Reading Ohmmeter — Questions and 
Problems. 



VM 



JOk 






241. Measurement of Resistance. — I. Fall of Poten- 
tial Method (Ammeter and voltmeter required). — This is a 
very simple method for measuring an unknown resistance 
directly by Ohm's Law when an ammeter, a voltmeter and a 
source of current are available. Suppose the unknown re- 
sistance, A, Fig. 220, is the arm- 
ature or field magnet of a dy- 
namo. Connect the resistance to 
be measured in series with the 
ammeter and the source of elec- 
tricity. Connect the voltmeter in 
parallel with, or across the resist- 
ance. Make simultaneous read- 
ings of both instruments. The 
unknown resistance is calculated 
from Formula (30) R = E-*-C. 

In using this method precau- 
tion must be taken not to pass 
a greater current through the object to be measured than it 
will carry without heating, ^f 257, otherwise a higher resist- 
ance than the true one will be measured. Generally the 
larger the current used, without heating, the greater the ac- 
curacy, because the voltmeter gives a higher reading. This 

247 



Q 



Fig. 220.— Fall of Potential 

Method for Measurement 

of Resistance. 



248 



PRACTICAL ELECTRICITY. 



is especially true for measuring low resistances and for which 
this method is quite suitable. A milli- voltmeter will give 
greater accuracy when the resistance is quite low, as, for ex- 
ample, the series field of a large dynamo which may be .0001 
ohm. On the other hand, when the method is applied to 
high resistances the current will be small and a milli-ammeter 
can be used to advantage. 

Prob. 99 : What is the resistance of the object A, Fig. 220, if the 
respective readings of ammeter and voltmeter are 4 and 36 ? 



By Formula (30) 



R=H=^_9ohms. 

C 4 — 

C = 4 amperes, E = 36 volts. 



J 



1 



Prob. 100 : The resistance of a bonded rail is to be measured by the 
above method. The current through the rail and its copper joint is 
500_ amperes, the drop across the joint is 25 millivolts. What is the 
resistance in microhms ? 

F 095 
By Formula (30) E = "g = ^ = .00005 ohm. 

E = 25 millivolts = .025 volt, C = 500 amperes. 

By Formula (12) .00005 X 1000000 = 50 microhms. 

242. Measuring the Resistance of Arc and Incandes 
cent Lamps While Burning.— The fall of potential method, 

•ff 241, is adapted to this 
measurement. Connec- 
tions are shown for 
measuring an arc lamp 
while it is burning, in 
Fig. 221, and for 
measuring the hot re- 
sistance of one or more 
incandescent lamps 
while burning, in Fig. 
214. 

Suppose the pressure 
across the arc is 42 volts 
and the current 10 am- 
42 -s- 10 == 4.2 ohms, 



"Lamp 



?n^ 



n 



n 



Ammefer 

Fig. 221, — Measuring the Resistance of an 
Arc Lamp While it is Burning. 



peres, then the hot resistance is 

Formula (30). This resistance is much less than when the 

carbon tips are in contact when the lamp is not burning. 

The resistance of carbon decreases with the temperature 

rise. 



MEASUREMENT OF RESISTANCE. 249 

Prob. 101 : A series arc-light dynamo is supplying a constant current 
of 10 amperes to a lamp circuit with a potential difference at the 
dynamo brushes of 2745 volts. Each lamp requires 45 volts and the 
resistance of the line is equal to the resistance of 1 lamp, (a) What 
is the resistance of the external circuit? (b) How many lamps are 
burning? (c) What is the resistance of 1 lamp? (d) How many 
lamps can be maintained by 1 electrical horse power? (e) How 
many electrical horse power are delivered by the dynamo? (f) 
What i3 the length of this series circuit if it is constructed of No. 6 
B. & S. copper wire? 

Solution : 2745 — 45 = 2700 = volts drop on all the arc lamps. 
45 = volts drop on the leads. 

-rg- = 60 lamps burning (b). 

45 
By Formula (30) jq = 4.5 ohms resistance 1 lamp (c). 

45 
By Formula (30) jq = 4.5 ohms resistance of line. 

Total resistance = (4.5 X 60) + 4.5 = 274.5 ohms (a). 

By Formula (62) watts per lamp = 45 X 10 =450. 
746 
^ = ].65 lamps per H. P. (d). 

By Formula (65) H. P. = ^- C = 2745 ^ ^ = 36.79 H. P. (e). 

ByFormula(23) L = g-*^_M. = 4 - 5 * j® 250 = 10947.63 feet (f). 
No. 6 B. &S.= 26250 CM. 

243. Measurement of Resistance.— II. Substitution 
Method {Galvanometer and graduated rheostat required.) — 
Connect the unknown resistance, X, and the galvanometer in 
series, and to one or more cells, 
preferably of the closed circuit 
type, as shown in Fig. 222. Note 
the deflection of the galvanometer 
needle. Now substitute the grad- 
uated rheostat for the unknown 
resistance and adjust it till the 
needle attains its former deflection. Fi §- 222 .-Substitution Method. 

The resistance in the rheostat is now equal to the unknown 
resistance, since the current through the galvanometer is the 
same as before, and the pressure also the same. 

If the unknown resistance is so small that the galvanom- 
eter needle is deflected off the scale, the rheostat may be 
inserted in series with the unknown resistance, and the resist- 



r-mm, — KjH 



250 



PRACTICAL ELECTRICITY. 



ance unplugged till a suitable deflection is obtained. Then 
the unknown resistance is removed and resistance added by 
the rheostat till the deflection is the same as before ; the re- 
sistance so added is equal to the unknown resistance. 

Prob. 102 : With the connections, as shown in Fig. 222, the de- 
flection of the galvanometer with the unknown resistance in circuit 
was 25°. With the rheostat substituted it was found necessary to 
unplug 47 ohms to obtain a deflection of 25°. Therefore, 47 ohms 
is the resistance of the unknown object. 

Prob. 103 : When a small incandescent lamp was connected for 
cold resistance measurement, as in Fig. 222, the needle was deflected off 
the scale. The rheostat was inserted in series and 55 ohms unplugged 
when 40 deflections were indicated. The lamp is now removed and 
the deflections are 47. It required 12 ohms to be added to the circuit 
to reduce the deflections to 40, therefore 12 ohms is the cold resist- 
ance of the incandescent lamp. 

244. Measurement of Resistance. — III. Drop Method 
of Comparison (A standard known resistance, or a graduated 
rheostat and a voltmeter required). — This method is very con- 
venient for many practical 
measurements. No ammeter is 
required. The known and un- 
f / unknown known resistances are connected 
AAJVlVJViVjW M\J\]\SV— ^ in series and to a source of con- 
stant current, Fig. 223. The 
drop across each resistance, as 
measured by the voltmeter, is 
directly proportional to that re- 
sistance, since the current is the 
same through both resistances. 
The drop on the known resistance 
also bears the same relation to the 
drop on the unknown resistance as the value of the known 
resistance bears to the value of the unknown resistance, or, 
calling the known resistance the standard and the unknown 
resistance X, then : 



VM 



STANDARD 

HNOWN 

RESISTANCE 



L l 



Fig. 223. — Measurement of Re- 
sistance by the Drop Method 
of Comparison. 



Drop on Standard 
Drop on X 



Resistance of Standard 



Or unknown resistance X = 



(89). 



Resistance of X 

Ees. of Standard X Drop on X 
Drop on Standard 

A high resistance galvanometer, the deflections of which 
are proportional to the current, may be used instead of the 
voltmeter and the value of the deflections substituted in the 



MEASUREMENT OF RESISTANCE. 251 

formula. In this method the current used should not be 
strong enough to heat the resistance appreciably. The most 
accurate results are obtained when the standard resist- 
ance is selected as near as possible to the supposed value of 
the unknown resistance. If the current is not very steady 
several readings should be taken of each measurement and 
the average value used in the formula. With suitable 
selected standards this method is adapted for measuring 
either high or low resistances with accuracy. 

Prob. 104 : With the connections as shown in Fig. 223, the drop on 
the standard resistance of 5 ohms was 2 volts, while the drop on the 
unknown resistance was 10 volts ; the unknown resistance then is 5 
times as great, or 25 ohms, or 

By Formula (89) Resistance of X = 5 * 10 = 25 ohms. 

245. Measurement of Resistance. — IV. Voltmeter 

Method ( Voltmeter of known resistance required). — This method 
is especially adapted for measuring high Batten 
resistances, as insulation of wires, etc. The 
voltmeter is connected directly across the 
source of E. M. F., which should be as high 
as possible, within the limits of the scale, 
and the deflection noted (which we will 
call d) by dosing the switch K, Fig. 224. £*£$ljE£E 
Switch K, is now open and the unknown by the Use of a Volt- 
resistance inserted in series with the volt- meter - 
meter (call this deflection d x ), and the resistance of the 
voltmeter, r. The formula for finding the value of the 
unknown resistance R is 

R = r (J--1) (90). 

Derivation of Formula (90).— Since the E. M. F. is constant, the 
drop through the voltmeter alone equals CXr which is also equal to 
the drop through the voltmeter and extra resistance or Cj R -f- C x r. 
The deflection d or d x , of the voltmeter needle is proportional to the 
current, therefore : 

dr = d x R -r-d.! r, 
transposing dr — d x r = d x R, 
dividing byd 1 ^-^ = E, 

or ^ -r = R, 
di 

or r([L —i)=R. 




252 PRACTICAL ELECTRICITY. 

Prob. 105 : When the voltmeter in Fig. 224, is directly connected 
across the source of E. M. F. 110 volts are indicated ; when placed in 
series with the unknown resistance, 4 volts are indicated, see Fig. 155. 
What is the value of the unknown resistance if the voltmeter has a 
resistance of 150000 ohms ? 

By Formula (90) R= r (^ 1) = 

d] 

150000 (^-1) = 150000 X (™ - |) = 

150000 X ^p = 3,975,000 ohms, or 3.975 megs, 
d = 110 volts, d x = 4 volts, r = 150000 ohms. 

246. Measurement of Resistance. — V. By Weston In- 
struments. — A number of practical applications of the fore- 
going methods are illustrated in a catalog issued by the 
Weston Electrical Instrument Company. 

247. Measurement of Resistance. — VI. Wheatstone 
Bridge (Principle of the slide wire pattern). — In Fig. 225 two 
unequal resistances, ab and cd, are connected in parallel and 
to a source of constant E. M. F. The drop across the wire, 

.Batten,, a<b, is equal to the drop across the wire, cd, 
say 3 volts between points 1 and 2, the 
drop for any given length on ab is, however, 
not equal to the drop on the same length 
3 of be, since the resistances are unequal. If 
some point as 3 is selected along ab, and 
c «'wwwwi/wvi/vk ^he difference of potential between this 
Fig. 225.— Principle point and a is 2 volts, then a corresponding 
of the Wheatstone point on cd can be found, as point 4, 
between which and c there will also be 
a difference of potential of 2 volts. This may readily be found 
by connecting one terminal of a galvanometer to point 3 and 
sliding the other terminal along cd until the galvanometer is 
not deflected when point 4 is found. Since there is no dif- 
ference in potential then between points 3 and 4, no current 
flows through the galvanometer, consequently its needle re- 
mains at zero. If a piece of heavy wire were connected to 
points 3 and 4 under these conditions, no current would flow 
through it, nor would the current in the circuit be disturbed. 
If after a balance is so obtained the slider at 4 is moved 
nearer to c, the current divides at 3 and part flows to points 
3 and 4 through the galvanometer, deflecting it to the right 
of zero, say, since the difference in pressure between c and 4 




MEASUREMENT OF RESISTANCE. 



253 



is less than 2 volts, while that between a and 3 is 2 volts. 
If, in the same manner, the slider at 4 is moved toward d, 
there is a greater drop across c-4 than a-3, and the current 
at 4 divides, part flowing to point 2 by 4-3 through the 
galvanometer, and deflecting its needle now in the op- 
posite direction, or to the left. When the balance of the 
galvanometer needle is obtained the volts drop across 
a-3 is equal to the drop across c-4, and the drop across 3-b 
equal to the drop across 4-d. The value of the resistance 
a-3 bears the same ratio to that of c-4 as resistance 3-b 
compared with 4-d. 

For example, if a-3 is 6 ohms and c-4 is 12 ohms, when 
a balance is obtained whatever is the resistance of 3-b, it will 
be just one-half as great as the resistance of 4-d. This ref- 
lation enables any unknown resistance, such as 3-b, to be 
measured when the others are known, by balancing the po- 
tential differences in the divided circuit by moving the sliding 
contact 4 to the point of balance. From the proportion, 



we get 



Res, a-3 _ Res. 3-b 
Res. c-4 Res. 4-d' 

Res . 3-b = Res- a-3 X Res. 4-d 
Res. c-4. 



When balance is obtained the values of the three resistances, 
a-3 5 c-4 and 4-d are substituted in the above formula and 
the unknown resistance, 3-b, is 
readily calculated. 

248. Lamp Chart Analogy 
of Wheatstone Bridge. — 

The balancing of potentials may be 
practically illustrated by a number of 
16-C. P. 50- volt lamps (50 ohms hot), 
arranged as shown in Fig. 226 and 
connected to a dynamo circuit. Two 
lamps are connected in series at A, 
making the total resistance 100 ohms, 
which is connected in series with 
two lamps connected in parallel at C, 
the joint resistance of which is 25 
ohms, Formula (43). The total resist- 
ance of A and C in series is, therefore, 
125 ohms. If 125 volts are maintained 
across points 1 and 2, the circuit, AC, 
will receive one ampere, the drop 







Fig. 226. — Lamp Chart Analogy 
of the Wheatstone Bridge. 



254 



PRACTICAL ELECTRICITY. 



across the lamps at A will be 100 volts and across the lamps at C, 25 
volts. The A lamps burn at normal candle power, but the C lamps, 
dimly since they get only % ampere each. 

Consider now the lower half of the circuit. At B, 4 lamps are con- 
nected in series so that resistance of B = 200 ohms, Formula (36) 
plus 1 lamp in series with them at D = 250 ohms for this lower 
circuit. The current therefore through B and D is one-half ampere, 
Formula (28), and all the lamps burn dimly since the drop across 
each lamp is only 125 h- 5 = 25 volts. The drop across B is therefore 
100 volts, the same as it was across A, and 25 volts across D, or the 
same as across C. Now since the drop across 1-3 is exactly the same 
as that across 1-4, 100 volts, if points 3 and 4 are connected b3 r a wire 
no current will flow through it and the lamps will burn with the 
same brilliancy as when 3 and 4 are not connected. If the resistance 
of the lamps is fairly uniform and a voltmeter is connected across 3 
and 4 it will not show any appreciable deflection. If the wire across 
3 and 4 is removed from 4 and placed, say to the right of the lamp at D, 



D 
Unknown 
Resistance 




Gauvan omete r 



Fig. 227.— Student's Slide Wire Bridge. 

Complete connections for measuring the unknown resistance at D are depicted. The 

student's Daniell cell and detector galvanometer are used. 

then the condition of balance is destroyed, the lamps at A are sub- 
jected to 125 volts and burn above c. p. while lamps at C are cut out of 
circuit and the wire 3-4 carries the current flowing through the lamps 
at A. 

This lamp chart should assist the student in understanding how the 
potentials are balanced in the slide wire bridge and the Wheatstone 
bridge, |" 250. 

249. Construction and Use of Slide Wire Bridge.— A 

simple form of slide wire bridge for measuring resistance is 
depicted in Fig. 227. A piece of German silver or platinoid 
wire, about No. 24, is stretched between binding posts, cd, 
mounted on a wooden base. Directly under the wire is a 
paper double scale about 22 inches long, graduated in 1000 
equal divisions with zero at either end, to facilitate taking 
readings from either point, c or d, 




MEASUREMENT OF RESISTANCE. 255 

Strips of copper mounted on the base, support additional 
posts for reception of the spool resistance terminals and serve 
to make electrical connections. The small letters and figures 
indicate the same points on this bridge as shown in the dia- 
gram, Fig. 225, by which its principle was explained, ^j 248. 
A resistance spool, with 
copper terminals, shown 
in detail in Fig. 228, and 
wound non-inductively, 
^f 299, is inserted in the 
binding posts at A, Fig. 
227, and corresponds to N( .,.., „„...,. 
the former resistance a-3. vv.nd.n6-. R«, S ta NC £ 5p <"»- s "°" 

The unknown resistance, Fi S- 228.— Details of Resistance Spool 

o -, , -. , ,i and Slider. 

o-b, is connected to the 

posts at D. The battery is connected across points 1 and 2, 
as before, and one galvanometer terminal to post 3, the 
other galvanometer post is connected to the flexible wire 
slider shown in detail in Fig. 228. The slider is moved 
along the wire, cd, till some point, as 4, is found where the 
needle is not deflected. 

When balance is obtained the unknown resistance is calcu- 
lated by the Formula in ^[ 248, as follows : 

Unknown Res. = Res " a-3 X length 4- d , 
length c - 4 

Referring to Figs. 227 and 229 : 

Let A = known resistance ; 

B = length of wire between c and point 4 w T hen balance is ob- 
tained ; 

C = length of wire between point 4 and d when balance is ob- 
tained ; 

D = value of unknown resistance. 

Then by the above formula, 

Resistance of D = Res " °f A * le " g th C (91). 

length B v ' 

More briefly D=^-^« 

Several different spools are furnished with the bridge, such 
as 1, 10 and 100 ohms, and the proper spool to be inserted at 
point A, should be as near in value to the resistance to be 
measured as can be approximated before measurement, The 
error in measurement is less when this is the case, 



256 PRACTICAL ELECTRICITY. 

The contacts should be clean and all wires fastened tightly, 
the slider should also be cleaned. Care must be exercised 
in moving the slider over the bridge wire so that it is not 
scraped, since the accuracy of measurement depends upon the 
uniform cross-section of the bridge w r ire. It is best to make 
several trial contacts at different points and note the direction 
of the needle's deflection, instead of running the slider along 
the wire. The same approximate pressure of the hand should 
be applied in making contact w r ith the slider in different 
measurements. One or two cells in series will be sufficient 
for ordinary measurements and a switch can be introduced 
into this circuit to prevent the current from heating the wire, 
and also to prevent polarization, when open circuit cells are 

used. The slide wire bridge is 
adapted for measuring low resist- 
ances and is a laboratory instru- 
ment; the Wheatstone bridge, 
If 250, is a commercial instrument 
for measuring high or low resist- 
ances. 

Prob. 106 : You are required to 
Fig. 229.— Slide Wire Bridge measure the resistance of a spool of 
Connections. wire which from rough calculation 

by Formula (22) is about 20 ohms. 
When inserted in the bridge thefollowing data is recorded when bal- 
ance is obtained : the 10 ohm spool was selected, B = 350 scale divi- 
sions read from the left-hand zero mark, C = 650 divisions read from 
right-hand zero mark. What is the value of the unknown resistance 
at D, Fig. 229 ? 

By Formula (91) D = A * C =- 10 * 650 = 18.57 ohms. 
±> 3o0 

A = 10 ohms, C = 650 divisions, B = 350 divisions. 
Prob. 107 : In another measurement with the slide wire bridge, A 
= 100 ohms, B = 100 divisions, C = 900 divisions. What is the value 
of the unknown resistance ? 

By Formula (91) D = ^-^ = 1 00 * 9Q0 = 900 ohms. 

Prob. 108 : What is the value of an unknown resistance measured 
by the slide wire bridge when A = 1 ohm, B = 900 divisions, C = 
100 divisions. 

By Formula (91) D = A * C = 1 ^ ^°° = .11 ohm. 

Problems 107 and 108 illustrate about the range of the bridge with 
the spools furnished, but the per cent of error in measurement in- 
creases as the resistance to be measured increases, and measurements 
are more accurate for low resistances with this type of bridge, 




MEASUREMENT OF RESISTANCE. 



257 



250. Student's Wheatstone Bridge {Lozenge Pattern) . — 
The Wheatstone bridge is based upon the same principle of 
balancing potentials in a divided circuit as explained in ^f 248. 

In Fig. 230 a simple diagram of the circuit is given. A, 
B, C, and D are called the arms of the bridge. The unknown 
resistance is connected at D, a variable rheostat at C, and re- 
sistance spools are inserted in the arms, A and B. The con- 
nections and apparatus required for making measurements by 
the student's lozenge bridge are illustrated in Fig. 232. One 
of the spools of the resistance set, which was previously cal- 
culated by Formula (22) is inserted in the D arm for verifica- 
tion of the calculation by electrical measurement. The ap- 
paratus illustrated comprises the following parts : lozenge 
bridge with spools, student's Daniell cell, adjustable graduated 
rheostat, double contact key, and detector galvanometer. The 
arms are lettered to correspond with the diagram, Fig. 231. 




Fig. 



230. — Principle of the Wheat- 
stone Bridge. 




-Principle of the Wheat- 
stone Bridge. 



The resistance in the arm, A, bears the same relation to that 
in B as the resistance in the rheostat at C does to the un- 
known resistance at D. Spools are selected for A and B 
and the resistance of C varied till the galvanometer needle 
stands at zero. 

A balance of the resistances in the bridge arms is illustrated 
in Fig. 231. The proportion is shown by the values of the 
resistances in the arms which is as 10 is to 100, so is 200 to 
2000, or 

Res. of A Res. C 



Res. of B Res. D 5 



Res. of D = 



17 



Res, of B X Res, of C 
Res. oi A 



258 



PRACTICAL ELECTRICITY. 



Res. of D = B * C 
A 



(92), 



Six spools are provided with this particular bridge ; 2 one-ohm, 
2 ten-ohm, and 2 one-hundred-ohm spools. For the proper 
selection of spools see the following paragraphs. 

The double contact key, Fig. 232, is practically two button switches 
mounted on the same base, the upper switch connected to the two ad- 
jacent posts marked B, closes the battery circuit when a slight pres- 
sure is applied. The lower switch is connected to the other two posts 



Rheostat. 




Double Contact Key ^Detector Galvanom eter 

Fig. 232.— Student's Wheatstone Bridge (Lozenge Pattern) with the 

Necessary Apparatus Required for Measuring Resistance. 

Connections should be made as depicted. 



MEASUREMENT OF RESISTANCE. 259 

marked G, and is inserted in series with the galvanometer, Fig. 232. 
When the button is depressed two independent circuits are closed in 
this order. On breaking the circuits the galvanometer circuit breaks 
first. The battery circuit must always be closed before the galvanom- 
eter circuit in order to allow the current to become steady before 
closing the galvanometer key, hence the use of the double contact key. 

251. Operating the Bridge. — Make the bridge connections 
as given in ^[ 250, and Fig. 232. Suppose the unknown re- 
sistance, a coil of wire connected at D, is about 20 ohms. Con- 
nect a 10 ohm spool in arms A and B. Connect the battery 
through the double contact key to posts marked B, likewise 
the galvanometer through the posts marked G. See that all 
connections are bright and tight. Insert resistance in the 
graduated rheostat to the value of what you suppose D will 
measure. Depress the double contact key and note direction 
of needle's deflection, say to the left. Release the key and add 
more resistance to the circuit by changing the position of the 
rheostat arm. If on depressing the key the deflection now is 
still to the left but less than before, release the key and add more 
resistance. If on the next trial the needle swings to the right, 
too much resistance has been added and some must be taken out 
of the rheostat circuit. Proceed in this manner till a balance 
is obtained. If on the first trial adding resistance had further 
increased the needle's deflection, too much had been taken 
out at the start. In the above case the needle swinging to the 
right of zero means that the rheostat's resistance must be de- 
creased while the needle swinging to the left of zero indicates 
too low a resistance in the rheostat. 

With the same pole of the battery always connected to the 
same bridge post, this relation of the needle's deflection will 
always hold good, and in such a case could be marked on the 
instrument, as is done in the portable bridge sets. Suppose a 
balance is obtained when 18 ohms are in the rheostat circuit. 

Then by Formula (92) D = 5-^ = ^^ = 18 ohms. 

When the A and B arms have equal resistances they will 
always cancel in Formula (92), so that the unknown resist- 
ance is then equal to the amount inserted in the rheostat 
circuit, and can be read directly from it without reference to 
the formula, With equal resistances in the A and B arms, 
which should always be as near as possible to the unknown 
resistance, the maximum resistance that the bridge will 



260 PRACTICAL ELECTRICITY. 

measure is limited to the resistance contained in the rheostat, 
which, in the student's rheostat, illustrated in Fig. 232, is 
160 ohms. 

252. To Measure a Higher Resistance Than That in 

the Rheostat. — By inspection of Formula (92) Res. of D = 

B X C 

— ^ — it will be observed that the value of resistance in the 

A 

A arm is the divisor, so that if a low resistance spool is selected 
for it and a high resistance spool for the arm, B, the quotient 
will be high. For example, let B = 100 ohms, A = 1 ohm, 
and suppose that balance against some unknown resistance 
was obtained when 150 ohms had been inserted in the rheo- 
stat, then 

D = 100x150 =15000ohmS) 

or the bridge is capable of measuring a much higher resist- 
ance than that contained in the rheostat. 

253. To Measure a Low Resistance. — 

In this case the divisor A, in Formula (92) should be very large 
and B small, hence select spools for arms A and B accordingly. For 
example, let arm B = 10 ohms, and A = 100 ohms and balance ob- 
tained against some unknown resistance when 2 ohms were inserted 
in the rheostat, then 

n B X C 10 X 2 20 . , 
D =— J— = "100" = loo = - 2 ohm > 
or the bridge will measure a much lower resistance than any con- 
tained in the rheostat. Suppose a balance is obtained in another 
measurement when B = 1, A = 100 and C = 2, 

then> D _ ILXC _ Oc_2 = ^ = .02 ohm. 

254. The Best Selection of Resistances for the Bridge 
Arms. — The best selection of spools for the greatest accuracy 
in measurement depends upon the resistance of the galva- 
nometer and the internal resistance and E. M. F. of the cells 
used with the bridge, so that no specific rule can be given 
beyond the varying of the ratios, as in ^|*ff 252 and 253. 

255. Commercial Wheatstone Bridge.— The student's 
bridge, illustrated in Fig. 232, is a laboratory form for teach- 
ing the principles involved. A portable commercial bridge 
is shown in Fig. 233. The case contains the rheostat, bridge, 
switch, and galvanometer. The unknown resistance to be 
measured is connected to the left-hand binding posts and the 



MEASUREMENT OF RESISTANCE. 



261 



battery to the right-hand pair of posts. In many portable 
bridges the battery is also contained withi n the case . 
sistance is inserted in the arms 
by removing the plugs, as shown 
in detail in Fig. 235. A general 
plan of the portable bridge and 
its connections is depicted in 
Fig. 234. The letters and figures 
correspond to the previous dia- 
grams, so that the lozenge may 
he traced out, though the parts 
are not arranged in the form of a 
lozenge. The A and B arms are 
provided with three different re- 
sistances, as in the student's type, 
which can here be used separately 
or all in series. The current 
divides at point 1 and unites 
again at point 2, and the galva- 
nometer is placed across points 
3 and 4, as in Fig. 230. The lozeng 
234 is further shown in detail in Fi 




lo o j o i 



CZ3 




Fig. 233.— Portable Wheatstone 

Bridge Set (Commercial Type). 

The galvanometer and rheostat are 

contained in this case. 

e principle of Fig. 
235. 
In using this type of bridge particular care must be ob- 
served to have the plugs 
tight, by giving them a 
slight twist to the right 
while inserting them. The 
galvanometer is delicate and 
the key should be tapped, 
rather than held down, so 
as to note the direction of 
deflection. This prevents 
the needle from being 
violently deflected when the 
system is not balanced. 
When a balance is nearly 
obtained the key may be 
held down for a longer 
time. For accurate measure- 
ments the current should not pass through the spools 
for any length of time, since their heating and consequent 
change in resistance is thus avoided. The choice of resist- 



a 



^ J JO ZO Z O SV / i 

* UMHMOWX 




&ATTERX 

Fig. 234.— Arrangement and Connections 

of the Portable Wheatstone 

Bridge Set. 



262 



PR A OTIC A L ELECTRICITY. 




Fig. 



235.— The Lozenge Diagram Applied to the 
Portable Wheatstone Bridge. 



ance arms and method of operating are as given heretofore. 
For measuring low and medium resistances one or two cells in 
series may suffice to operate the bridge. The higher the 
E. M. F. used the more accurate the results. For very high 

resistances,, insula- 
tion resistance, etc., 
a number of cells, 
generally mounted 
in a separate case, 
^[ 92, are employed. 
256. Direct 
Reading Ohm- 
meter. — This in- 
strument measures 
automatically the 
resistance of any de- 
vice that may be 
connected to its ter- 
minals. The resist- 
ance can be directly 
read from the dial of the instrument when the battery circuit is 
closed. An ohmmeter indicates the relation existing between 
the potential difference at the ends of a conductor and the cur- 
rent flowing through it, since the resistance in ohms is the ratio 
of volts -5- amperes, Formula (30). The principle of action is 
as follows : Two coils, A, A, Fig. 236, are connected in series 
and to the source of current 
used in making the measure- 
ment, generally several cells 
for low resistance and a mag- 
neto, *\\ 322, for high resist- 
ance. Between these coils is 
suspended between jewel 
bearings a movable coil, B, 
at an angle to the coils A. A. 
The movable coil and resist- 
ance to be measured are con- 
nected in series and in 
shunt with the stationary coils A, A 




Fig. 236.— Construction and Connections 
of a Direct Reading Ohmmeter. 

This connection is 
made by joining the unknown resistance to the binding posts 
1-2. Current is led to the movable coil by the springs, S 3 as 
in the case of the Weston movable coil, Fig. 198. 



MEASUREMENT OF RESISTANCE. 263 

When the instrument is connected to the unknown resist- 
ance the current divides at point 4 in proportion to the resist- 
ances of the two circuits, and since the axes of the coils are 
at an angle, the movable coil tends to turn against the action 
of the springs so that its lines of force are in the same direc- 
tion as the lines of force of the stationary coils. A pointer 
fixed to the movable coil swings over a scale graduated in 
ohms. With a low resistance connected to the instrument, 
the field of the movable coil is strong and that of the station- 
ary coil weak, since the current divides between the two 
paths in proportion to the resistance. As the external re- 
sistance to be measured becomes higher, thus decreasing the 
current through the movable coil, the field of the stationary 
coil becomes stronger, so that the movable coil continues to 
be deflected and a very uniform scale is obtained. By using 
two sets of independent windings on the stationary coils, the 
instrument may be constructed with a double scale. The 
external appearance of the Weston portable ohmmeter is simi- 
lar to that of the Weston voltmeter. Fig. 212, except that the 
push button is omitted and there are four or more binding 
posts. In one size of double scale instrument the capacity is 
to 50 and 50 to 100 ohms, in one ohm divisions, and the in- 
strument is to be used with an E. M. F. of 2 volts. For 
measuring high resistances, as the insulation of wires, a 
magneto-generator is used, capable of generating several 
hundred volts, and the scale of the ohmmeter graduated in 
megohms. 

In some types of ohmmeters the magneto is mounted in the 
case with the instrument. When the value of the unknown 
resistance is not desired a magneto machine ^T 322, is often 
used to test for insulation. The E. M. F. is several hundred 
volts but the current it will give is very small on account 
of its high internal resistance. A magneto is rated according 
to the value of the resistance its E. M. F. can maintain suffi- 
cient current through to ring a bell in series with it. For ex- 
ample, a 20000-ohm magneto means that if the insulation be- 
ing tested is less than 20000 ohms, the bell will ring, thus in- 
dicating the fact. The higher the rating of a magneto the 
greater will be its E. M. F. 



264 PRACTICAL ELECTRICITY. 



QUESTIONS. 

1. What is the fundamental principle in the working of the Wheat- 
stone bridge ? 

2. The highest and lowest resistances in the rheostat of a Wheat- 
stone bridge are 10000 and .1 ohms respectively. The A and B arms 
have each 1, 10, and 100 ohm coils. What are the highest and lowest 
resistances the bridge is capable of measuring? 

3. Make complete sketch of a slide wire bridge connected up to 
measure the resistance of 10 pounds of No. 10 B. & S. copper wire. 

4. How does an ohmmeter differ from a Wheatstone bridge ? Upon 
what principle does it operate ? Make sketch. 

5. One terminal of a magneto is connected to an electric light wire 
and the other to the ground. When the armature is revolved the 
bell fails to ring. What does this indicate ? 

PROBLEMS. 

1. The drop across the series field coil of a dynamo carrying 250 
amperes is .7 volt. What is its resistance ? Ans. .0028 ohm. 

2. A rheostat, battery, galvanometer and unknown resistance are 
joined in series. With 40 ohms unplugged the deflections are 33. The 
unknown resistance is cut out of circuit and 45 additional ohms are 
inserted to reduce the deflection to its former value. What is the 
value of the unknown resistance? Give sketch. Ans. 45 ohms. 

3. You are required to measure the insulation resistance of an 
electromagnet using a proportionate deflection detector galvanometer, 
sensibility .00001 ampere for one degree and a 250 volt power circuit. 
The needle is deflected 3 degrees. What is the insulation resistance ? 
Give sketch. Ans. 8,333,333 ohms or 8.3 megs. 

4. The field magnets of a dynamo having a resistance of 84 ohms 
are connected in series with the field magnets of another machine and 
a current sent through the circuit. The drop on the latter field coils is 
111 volts, and on the 84-ohm coils, 37 volts. What is the resistance of 
the second set of field magnets ? Give sketch. _ Ans. 252 ohms. 

5. An insulation test of a 110-volt multiple circuit is made with a 
Weston voltmeter (resistance 150000 ohms). The voltmeter indica- 
tions are : positive to earth, 2 volts ; negati veto earth, 5 volts. What 
is the insulation resistance of each lead? Give sketch. Ans. Posi- 
tive, 8.1 megs ; negative, 3.15 megs. 

0. Balance is obtained in a Wheatstone bridge when A = 10 ohms ; 
B = 100 ohms ; rheostat 14 ohms. What is the value of the unknown 
resistance ? Give sketch. Ans. 140 ohms. 






LESSON XXII. 

ELECTRICAL DEVELOPMENT OF HEAT. 

Heating of Conductors and their Safe Carrying Capacity — Table XV. 
Current Carrying Capacity of Copper Wires — Electrical Develop- 
ment of Heat — Electrical Equivalent of Heat : Joule's Law— Re- 
lation Between Heat, Mechanical and Electrical Energy — Rela- 
tion of Fahrenheit and Centigrade Thermometer Scales — Relation 
of Resistance to Temperature — Table XVI. Temperature Co- 
efficients — Fuses and Cut-Outs — Table XVII. Gauges of Different 
Wires Fused by 100 Amperes — Electric Cautery, Blasting, 
Welding, and Cooking — Questions and Problems. 

257. Heating of Conductors and Their Safe Carrying 
Capacity. — Heat is caused by the molecules of a body being 
set in motion. To produce this motion the expenditure of a 
definite amount of mechanical energy is required. When a 
current of electricity passes through a wire, a certain amount 
of work is performed in overcoming the resistance of the 
wire, and this work appears as heat generated, according to 
the principle of conservation of energy, If 219. This fact 
becomes very noticeable when the wire is small and the cur- 
rent large ; the wire may then become so hot that it is melted 
by the current, ^| 97. The increase in the temperature of a 
wire due to the current, depends upon its weight or sectional 
area. For example, consider two copper wires, one weighing 
one pound, and the other twice as long but weighing four 
pounds, offering, therefore equal resistance to a current passed 
through them. The wires will not be raised to the same 
temperature, although the amount of heat evolved in each 
case is exactly the same. This is true because there is more 
metal to heat in one case than in the other. Thin wires, 
therefore, heat much more rapidly than thick ones of a like 
resistance when traversed by the same current. Since the 
resistance of metals increases as their temperature rises, a 
thin wire will have its resistance increased as it becomes 
heated, and will continue to grow warmer and warmer until 
its rate of loss of heat by conductance and convection to the 
surrounding air equals the rate at which the heat is evolved 
by the current. 

265 



266 



PRACTICAL ELECTRICITY. 



Exp. 67 : When a chain made of alternate links of platinum and 
silver wire of the same size, is connected to several cells joined in 
series, the platinum links become red-hot but the silver links remain 
comparatively cool. The resistance of platinum is about 6 times as 
great as silver, but its capacity to absorb heat only about one-half as 
great, hence its rise in temperature is about twelve times as great as 
that of the silver for the same current. 

The rise in the temperature of a bare wire in air is usually 
greater than that of the same wire covered with insulating 
materials. The effect of the latter is to increase the surface 
from which the heat is radiated and carried away by convec- 
tion. Wood being a very poor conductor radiates little heat, 
so that less current should be allowed for wires in wooden 
mouldings. The heating of a wire by a current is not objec- 
tionable except that it increases the loss of energy by the rise 
in resistance. The real limit of the current carrying capacity 
of a wire is at such a rise of temperature that the insulation 
is liable to be damaged. The National Electrical Code of the 
Fire Underwriters allows an elevation of temperature above 
the surrounding air of 27° to 30° F. for rubber covered 
wires used in carrying electric current. Figures are given in 
the following table for this elevation. The current can be 
increased nearly 60 per cent above these conservative figures 
without any injurious effect. Wires with " weatherproof " 
insulation will carry still more current, since they are not so 
readily affected by heat. 

Table XV.— Current Carrying Capacity of Copper Wires. 



B.&S. 


Amperes. 


B.&S. 


Amperes. 


18 


3 


4 


65 


16 


6 


3 


76 


14 


12 


2 


90 


12 


17 


1 


107 


10 


24 





127 


8 


33 


00 


150 


6 


46 


000 


177 


5 


54 


0000 


210 



The carrying capacity of copper wires used in dynamos 
varies from 600 to 1000 circular mils per ampere, according 
to the amount of ventilation the wire may receive. A much 
larger allowance must be made for contact surfaces in a 



ELECTRICAL DEVELOPMENT OF HEAT 267 



circuit, as between the brushes of a dynamo and the commu- 
tator, the clips of a switch, etc. ; about 100 amperes per 
square inch of contact surface is an average value. Switches 
are constructed and rated according to their carrying ca- 
pacities. 

258. Electrical Development of Heat. — I. Heat De- 
veloped is Directly Proportional to the Resistance of 
the Circuit. — In Fig. 237 two independent glass bulbs are 
connected with a graduated glass U tube and fastened to a 
suitable base by the vertical brass arm, B-2. Platinum 
wires are inserted in each bulb through a cork and connected 
to the binding posts, 1, 2, 3, as 
shown, post 3 being a common 
terminal for the wires in both 
bulbs. Suppose the wire, BC, in 
the right-hand bulb is exactly 
double the length of the wire in the 
left-hand bulb, but of the same 
size. Partially fill the graduated 
U tubes with water, close the 
stop-cocks and connect several 
cells in series to posts 1 and 3, 
when both platinum wires will 
be in series and the current the 
same through each of them. 
Permit the current to flow for a 
short time. The column of wa- 
ter in the open side of the right- 
hand U tube rises to about double 
the height above the normal 
position that the column in the left-hand tube does. A 
gas under constant pressure expands by a definite fraction of 
its volume for a given increase of temperature, consequently 
the air in the bulb, BC, must have been raised to double 
the temperature of that in the bulb, AB, or double the 
quantity of heat must have been evolved from the wire 
of twice the length, by the current. The heat generated in any 
wire is directly proportional to its resistance. In a cell furnish- 
ing current to an external circuit, twice the heat is evolved 
from the inside of the cell, if the plates are separated to twice 
their original distance and the current the same in both 
cases. 




Fig. 237.— Apparatusfor Studying 
the Laws Governing the Heat- 
ing Effect of an Electric 
Current. 



268 PRACTICAL ELECTRICITY. 

2. Heat Developed is Proportional to the Square of 
the Current. — To prove this statement, connect an ammeter 
in series with either of the bulbs in Fig. 237 by using two 
adjacent posts, 1-2 or 2-3. Note the value of the current in 
amperes, and the corresponding number of cubic centimeters 
rise of the level of the liquid in the U tube in a given time. 
Now double the current strength, and the liquid in the U tube 
rises, not to twice the former height, but to four times the 
former height in the same time. If the current is tripled 
the liquid rises to nine times the height recorded in the first 
test, and when quadrupled to sixteen times the first height, 
etc. For example, one ampere produces 3 divisions rise ; 2 
amperes produce 12 divisions rise ( (2x2) X 3) ; 3 amperes 
produce 27 divisions rise ( (3 X 3) X 3), all tests being run 
for the same length of time. The heat developed is directly 
proportional to the square of the current. 

3. Heat Developed is Directly Proportional to the 
Time. — This statement is so apparent that it need not be 
further considered. 

259. Electrical Equivalent of Heat. — Joule's Law — 
Dr. Joule first discovered that the development of heat was 
proportional to : 

1. The resistance of the conductor ; 

2. The square of the current ; 

3. The time during which the current flows. 

The heat (H) developed in a unit of time is directly propor- 
tional to the amount of power expended in overcoming the re- 
sistance of the conductor, or to the product of current C, through 
the conductor, and the difference of potential E between its ex- 
tremities, or H = E X C. If the resistance of the wire re- 
mains constant, the value of C varies directly as E, so that 
by doubling E, C will also be doubled or the heat developed 
will be proportional to the square of the current as experi- 
mentally demonstrated in ^| 258. The British Thermal Heat 
Unit {written B. T. U.) is defined as the amount of heat required 
to raise one pound of water 1° Fahrenheit {written 1° F.) at its 
maximum density. 

A P. D. of 1 volt maintained across a resistance of 1 ohm for 
one second develops .0009477 of such a unit. The number of 
heat units developed in any number of seconds therefore is, 



ELECTRICAL DEVELOPMENT OF HEAT. 269 

Heat Units (H) = .0009477 X E X C X t . . . (93). 
t = the time in seconds. Substituting for E its value 

CXR, 

then H = .0009477 C 2 R t (94). 

Also since W = C 2 R, 

H =. 0009477 X watts X seconds (95). 

To Find the Total Heat Units Developed in a Given 
Time in any Circuit : 

Multiply the watts expended by the time the current flows and this 
'product by .00094.77, as in Formula {95). Formula (94) will 
give the same result.* 

Prob. 109. — How many heat units are evolved in one-half hour by 
a 110- volt incandescent lamp consuming a current of J ampere? 
By Formula (93) H = .0009477 X E X C Xt = 

.0009477 X 110 X -5 X 1800 = 93.8223 heat units. 
E = 110 volts, C = J ampere, t = J-hour = 1800 seconds 

To Find the Current Required to Produce any Given 
Number of Heat Units by a Known E. M. F. in a Given 
Time : 

Use the following formulae derived directly by transposition from 
Formula (93) : 

^ — f\c\c\c\Ann w -cv w + (96). 



.0009477 X E X t 

H 

.0009477 X E X C 



(97), 



Prob. 110: A 110-volt J-ampere incandescent lamp is immersed in 
a vessel containing 1 pound of water. How long a time will be re- 
quired to raise the water to the boiling point ? The temperature of 
the water before the test is 60° F. Neglect losses, due to radiation, 
etc., and assume that all the energy is converted into heat. 

Solution : The water must be raised 212° - 60° =152°. 
1 lb. X 152 = 152 heat units to be given to the water. 

By Formula (97) t = . 009477XExC = . 0009477 X 110 X. 5 = 2916 sec ' 
-nrr- = 48 min. 36 sec. till water boils. 

Prob. Ill : What current will be required by a lamp immersed 
in the above pound of water to boil it in one-half hour? The E. M. 
F. is 110 volts ; heat losses to be neglected. 

Solution : Solve by Formula (96). Ans. 0.8 ampere. 

*If the Centigrade scale is used and the gramme unit employed, then Formula (93) 
becomes H = .24 EC t, since .24 heat unit is evolved by one watt in one second. In this 
case the heat unit is called the calorie, and is the amount of heat required to raise one gramme 
of water one degree. 



270 



PRACTICAL ELECTRICITY. 



260. Relation Between Heat, Mechanical and Electri- 
cal Energy. — Referring to H 217, Formula (60) etc., we 
find that the electrical work performed in a circuit is propor- 
tional to the same factors as the heat development, Formula 
(94). This is true, since the electrical work appears as heat. 
The following problem will illustrate the relation between 
electrical work, in joules, % 217, and electrical heat, in heat 
units or B. T. U. 

Prob. 112 : A current of 4 amperes flows through 2 ohms for 3 
seconds, (a) Find the work performed in joules, (b) Find the 
number of heat units developed in the circuit. 

By Formula (60) J = C 2 R t = 4X4x2X3=96 joules (a). 

By Formula (94) H = .0009477 C 2 R t =.0009477 X4X4X2x3 = 
.0909792 heat unit. 
h- « Therefore 96 joules = .0909792 heat unit ; 

| J 1 joule =.0009477 heat unit, 

a h The relation between mechanical energy, electrical energy 

and heat energy, ^ 220, is then as follows : 

Mechanical Energy — Electrical Energy — 
778 foot-pounds = 1005.2 joules = 
Heat Energy. 
1 B. T. U. 

261. Relation of Fahrenheit and Centi- 
grade Thermometer Scales. — Since both of 
these scales are much used in referring to the 
resistance of a wire at a particular tempera- 
ture, the relation between them is given by the 
formulse below, and also shown diagramatically 
by Fig. 238. On the Fahrenheit scale the 
melting point of ice is placed at 32° and the 
boiling point at 212°, while on the Centigrade 
scale the melting point of ice is placed at zero 
and the boiling point at 100°. Therefore 100° 
C. = 212 — 32 = 180° F. or the ratio of C.° to 
Fig. 238.— F.° is as 5 to 9. In converting a Centigrade 
Comparison of reading into a Fahrenheit reading 32 must be 
and Centigrade added, since the zero is 32° below Centigrade, 
Thermometer an d conversely 32 must be subtracted from a 
Scales. Fahrenheit reading. 

1. To Convert Fahrenheit to Centigrade : Subtract 82, 
multiply by 5 and divide by 9. 



l£ 


o 


JBoUinq Point 


eie-= 


— loo 






200 4 






— 90 


190 -1 




180 \ 


=- SO 


170 4 








I60-| 


1 70 


I50-| 




140 4 


~- eo 






• 30 4 




120 4 


1 50 


1 I04 




•oo 4 


=- 40 






90 4 


=- 30 


80-1 




70 4 


~ T eo 


60 4 




50 4 


r '0 


40 4 




32>= 


— o 


Freez 


ticj Point 



( F° — 32) 5 
9 



ELECTRICAL DEVELOPMENT OF HEAT. 271 

2. To Convert Centigrade to Fahrenheit : Multiply by 
9, divide by 5 and add 82. 

F = C ^-^-f32 (99). 

o 

Prob. 113 : A field magnet spool is stated to have a resistance of 
25 ohms at 15.5° C. Express this temperature in degrees Fahrenheit. 

By Formula (99) F° = ( ^ < - 9 + 32 = 15 - 5 5 * 9 -f 32 == 59.9 or 

nearly 60° F. 

Prob. 114 : The resistance of a unit foot of copper wire was stated 
to be 10.79 ohms at 75° F. What is the corresponding temperature 
in the Centigrade scale ? 

By Formula (98) C° = (F °~ 32) 5 = ( 75 ~ 3 Q 2 ) x5 = 2 4° C nearly. 

262. Relation of Resistance to Temperature.— Refer 

to Law V of the Laws of Resistance, ^[ 127, for the relation 
of temperature to resistance of wires. The percentage change 
of resistance of a wire with a unit change of temperature is 
known as the temperature coefficient. For example, the resist- 
ance of 1000 feet of wire one-tenth inch in diameter is about 
1 ohm at 76° F., Fig. 102, and at 100° F. the resistance is 
increased to 1.0525, while at 50° F. the resistance is only 
.9475 of an ohm. This change in the resistance of a wire 
due to the temperature rise or fall is a very important matter 
in electrical calculations and measurements, and must always 
be taken into consideration. The following formulae and 
temperature coefficients will enable the student to calculate 
the resistance of different metals at different temperatures : 
Let R = the original resistance ; 

R x = the resistance after a rise or fall in temperature ; 

F° = number of degrees rise or fall ; 

T = the temperature coefficient for Fahrenheit scale 
or the change per degree per ohm. 

The formula for finding the increase in resistance due to a rise 
in temperature is : 

R, = (RXTX F° Rise) + R (100). 

And the formula for afcdl in temperature is : 

R 1= =R — (R X TxF°fall) (101). 

When the Centigrade scale is used select the temperature co- 
efficient (T) for this scale and substitute C° for F° in the above 
formulas. The following temperature coefficients (values of 



272 



PRACTICAL ELECTRICITY. 



T) are given for some metals. The figures represent the 
amount 1 ohm would increase or decrease in resistance 
when subjected to a rise or fall of so many degrees F. or C. 
For example, 1 ohm of copper wire for a rise of 1° 
F. has a resistance of 1.0021; 10 ohms for 1° = 10.021; 
or 10 ohms for 10°-= 10.21 by Formula (100). 

Table XVI. — Temperature Coefficients. 





Metal. 


(Values of T.) 




Fahrenheit 
Scale. 


Centigrade 
Scale. 


Silver 


. 00209 i 
.002156 
.002167 
.001372 
.002517 
.002028 
.002150 
.001967 
.000489 
.000244 


00377 




00388 




00390 


Platinum 


00247 




00453 


Tin 


00365 


Lead 


.00387 


Bismuth 

Mercury 

German silver 


.00354 
.00088 
.00044 



The resistance of copper wire thus increases nearly one- 
quarter of 1 per cent (.0021) for each degree F. for each 
ohm, and iron wire more than one-quarter of 1 per cent 
(.002517). 

Prob. 115 : The resistance of the field magnets of dynamo is 55 
ohms at 70° F. ; after a ten-hour run the temperature of a thermome- 
ter placed against them, for a short time, is 94°. (a) What is their 
resistance at this temperature? (b) What would be the resistance at 
40° F.? 

By Formula (100) R x = (R X T X F.° rise) + R = (55 X .002156 X 

24) + 55 = 57.845 ohms (a). 
R = 55 ohms, T for copper wire = .002156, F.° =94 - 70 = 24° rise. 
By Formula (101) R,= R - (R X T X F.° fall) = 55 -(55 X .002156 

R = 55 ohms, T=. 

263. Fuses and Cut-Outs. — When a piece of copper and 
lead wire of the same size are connected in series and a current 
passed through them so that their temperature is increased, the 
lead will melt when a temperature of 612° F. is attained, while 



,= R- 


(RX TXF. C 


fall) 


= 55-(5 


X 30) = 


= 51.442 ohms (b). 




002156, 


F.o = 70° _ 


40° = 


= 30° fall. 



ELECTRICAL DEVELOPMENT OF HEAT 273 




it will require a temperature of 1996° F. to melt the copper. 
Lead containing a small percentage of tin is used for electric 
fuses on account of 
the low tempera- 
ture at which it 
melts. A fuse con- 
sists of such a lead- 
en wire or strip 
which is inserted in 
series with the cir- 
cuit it is desired to 
protect, and de- 
signed so as to melt, 
and thus automati- 
cally open the cir- 
cuit when the cur- 
rent through it becomes excessive. The fuse is mounted on 
a porcelain block and the appliance termed a cut-out. The 
canning capacity of a fuse depends upon its cross-section, 
and fuse wire is generally rated to be of so many amperes 
capacity, meaning that it will carry this current without 
melting or " blowing," as it is termed, and melt on a slight 
increase in current above its capacity. The function of a 
fuse, therefore, is to open the circuit before the temperature 
rise due to an excessive current from any cause, has oppor- 
tunity to heat the conductors. A circuit breaker, Fig. 176, 
performs the same function. The gauges of different wires 
fused by a current of 100 amperes, is given in the following 
table : 



Fig. 239.— Copper Tipped Link Fuses for Cut-Outs. 



Table XVII.— Gauges of Different Wires Fused by 100 Amperes 

(Preece). 



Copper No. 17B.&S. 
Aluminum 15 " 

Platinum 13 " 

German Silver 13 " 
Platinoid 12 " 



Iron 
Tin 

Lead 
Tin Alloy 



No. 



10B.&S. 

6 " 



264. Electric Cautery, Blasting, Welding and Cooking. 

In surgery a thin platinum wire heated to a white heat by 
the current is used for many operations instead of a knife. 
18 



274 PRACTICAL ELECTRICITY. 

Platinum is chosen because it is the most refractory metal 
but is readily fused when the current is too strong. 

In blasting, the fuse is surrounded by some combustible 
material in proximity to the explosive. A current sent from 
a distant battery, through copper wires, melts the fuse or 
heats the platinum wire, as the case may be, and the combus- 
tible is ignited and the powder exploded. 

In electric ivelding the terminals of the parts to be joined, form 
the electrodes of the source of supply, which is generally of a 
low voltage but capable of giving a large volume of current. 
When the circuit is completed at the electrodes most of the 
energy is expended at this junction, since it is of higher re- 
sistance than the other parts of the circuit, and appears as 
heat. The current in such operations is often obtained from 
transformers and may be several hundred amperes at a few 
volts pressure. 

In the water-pail system of welding a direct current of about 
200 volts is used and the metallic tank containing, for exam- 
ple, a solution of ordinary washing soda, is connected to the 
positive pole of the supply source. The tongs are connected 
to the negative pole and the piece to be heated clamped in 
them and immersed in the solution when it becomes heated 
to a welding heat. The heating is due to the film of hydro- 
gen which collects around the negative pole (by electrolysis, 
^f 100) and greatly increases the resistance at that point. In 
welding, two pair of tongs connected to the negative pole may 
be used simultaneously. 

In electric cooking utensils, iron or other high resistance wire 
is wound around some insulator of electricity, as a porcelain 
or asbestos tube, and these coils inserted in the utensil desired. 
The heat is radiated to some good heat conductor in the vi- 
cinity of the coils, as for example, the copper bottom or sides 
of an electric tea-kettle. The wire is proportioned so that it 
will contain sufficient resistance to be placed in multiple with 
an incandescent lamp circuit and permit enough current to 
flow through it to maintain a temperature somewhat below its 
fusing point. A good heat conductor, as copper, may be coated 
with some insulating enamel and the wire wound directly 
upon it. This method is used in some makes of rheostats, 
T{ 163. The advantage is that the heat is radiated so rapid- 
ly that the wire will carry a much larger current than under 
other conditions. 



ELECTRICAL DEVELOPMENT OF HEAT 275 

QUESTIONS. 

1. A cell is short-circuited by a thick piece of copper having a low 
resistance as compared with that of the cell ; the current from the 
cell is a maximum. Where will the most heat be developed ? 

2. Cite an experiment to prove that heat developed in a circuit is 
proportional to the square of the current. 

3. Equal lengths of No. 10 and No. 20 B. & S. copper wire are con- 
nected in series and to a cell. Is there any difference in the strength 
of current through, or heat evolved from, either wire? 

4. A thermometer is immersed in a vessel containing dilute sul- 
phuric acid and a plate of zinc and copper. When the extremities 
of the plates are connected by a wire the temperature rises. Explain 
this. 

5. The size of wire for carrying 62 amperes with rubber covered 
insulation is calculated to be, in a certain instance, No. 6 B. & S. 
Would you use this size of wire ? Why ? 

PROBLEMS. 

1. How many heat units are evolved in 10 hours from an arc lamp 
requiring 10 amperes and 45 volts ? Am. 15352.74. 

2. How many pounds of water can be raised from 80° Fahr. to 
boiling point by the heat evolved in Problem 1, neglecting all losses ? 
Am. 116.3 lbs. 

3. With an E. M. F. of 110 volts what current must be passed 
through a coil of iron wire, immersed in 2 pounds of water so that it 
will boil in 45 minutes? The temperature of the water at the start 
is 60° Fahr. Am. 1.08 amperes. 

4. The hot resistance of an electrical laundry iron is 22 ohms and it 
is connected across a 110- volt main. Suppose the iron to be thrown 
into a vessel containing 4 quarts of water, the temperature of which 
is 60° Fahr., and the current turned on for 15 minutes. What will 
be the temperature of the water at the end of the time, not deducting 
losses for radiation, etc? Am. 117.27° Fahr. 

5. Give the equivalent amount of energy in joules and foot-pounds 
expended in the arc lamp in question 1. Am. 16,200,000 joules ; 
11,947,500 foot-lbs., or 11,946,902 foot-lbs. 

6. The length of the Institute concentric power cable, laid in ducts 
under Broad street, is 300 feet ; the size of conductor, No. 4 B. & S. ; 
suppose that the temperature in the ducts on a warm summer day is 
104° Fahr., and during a blizzard in winter, 40° Fahr. (a) What will 
be the resistance of the cable in each case ? (b) If the cable is deliver- 
ing 30 Kilowatt at 1100 volts, what will be the lost power on the line, 
at the summer temperature as above ? (c) What will be the cost of 
this loss, running 5 hours a day for 6 months (180 days) at 7| cents 
per horse-power-hour? Am. (a) .1647 ohm at 104° Fahr.; .1434 ohm 
at 40° Fahr. ; (b) 122.479 watts ; (c) $11,082. 



LESSON XXIII. 

ELECTRODYNAMICS. 

Reaction of a Current-Carrying Wire on a Magnet — Automatic 
Twisting of a Current-Carrying Wire Around a Magnetic 
Pole— Rotation of a Current-Carrying Wire Around a Mag- 
netic Pole — Electrodynamics— The' Magnetic Fields of Parallel 
Currents — Laws of Parallel and Angular Currents — Currents in 
Angular Conductors — The Electro-Dynamometer — Portable Dy- 
namometer Ammeter — Dynamometer Wattmeter — Thomson Re- 
cording Wattmeter — Questions. 

265. Reaction of a Current-Carrying Wire on a Mag- 
net. — Every action is accompanied b}^ an equal and opposite 
reaction, or, "action and reaction, are equal and opposite," 
% 57. For example, you elongate a spring in one direction 
by applying a force of one pound ; the spring also exerts an 
equal force in the opposite direction, or else it would break. 
A ship displaces an amount of water which is equal to its 
own weight, the force of buoyancy is therefore equal and op- 
posite to the force exerted by the weight of the ship, or else 
it would sink. In Lesson XV it was shown how a 
magnet was deflected by the magnetic field of a wire carrying 
a current. When the current flows over the needle, say from 
N to S, and the needle is free to move, the N-end is urged by 
the current's field to the east and the S-end, to the west. Since 
the field of the wire repels the magnet's field the magnet's 
field also repels the field of the wife, and if it w r ere free to 
move it would move in the opposite direction to that of the 
magnet. In ^[ 170 the right-hand rule was given for the 
direction in w T hich the needle would turn, the following rule 
employing the left hand will indicate the direction that the 
wire will move when the magnet is stationary. Arrange the 
wire over the needle and place the palm of the left hand over the 
wire as before, °\\ 170 ; the outstretched thumb at right angles to 
the hand will indicate the direction the wire will move. 

Exp. 68 :— Insert the rectangular coil of a single turn of wire, Fig. 
148, in the ampere frame, as shown in Fig. 240. Arrange the hori- 
zontal portion of the coil in the magnetic meridian, and by the use of 
.276 



ELECTRODYNAMICS. 



211 



a pocket compass find the direction of current around the wire. Open 
the circuit and lay a bar magnet on the ampere frame base, arranged 
so that the current flows over it from N to S, as in Fiu\ 240. The 
magnet is now stationary and the wire free to move. When the cur- 
rent flows through the wire it is de- 
flected west. Apply the left-hand 
rule, U 265, to this case. 

Exp. 69 : Explore the magnetic 
field both inside and outside of the 
rectangular coil by noting how the 
wire moves when the magnet is 
brought into its vicinity. The wire 
tends to move in all cases to such a 
position that its own lines of force are 
in the same direction as those of the 
field of the magnet. 

266. Automatic Twisting 
of a Current- Carrying Wire 
Around a Magnetic Pole. — That 
a wire tends to move so that its 

magnetic field 

will' be in the 

same direction 





Fig. 240.— The Movable Current- 
Carrying Coil is Repelled by 
the Stationary Bar Magnet. 



Fig. 241.— The Flexi- 
ble Tinsel Wire Winds 
Around the Magnet 
when a Current is Sent 
Through it. 



itself around the 
that the polarity at 
field as before. 



as the lines of force of the magnet's field 
is further demonstrated as follows : a bar 
magnet is clamped vertically in a stand 
and raised several inches from the table, 
Fig. 241, a connector is clamped above it, 
and a piece of tinsel wire, which is a very 
flexible conductor, is supported from the 
connector and connected to a battery as 
shown. When the current is sent up the 
wire from A to B, the wire twists or winds 
itself around the magnet in a left-hand 
s spiral, that is, so that the current cir- 
\ culates around the magnet anti-clock- 
wise as viewed from the N-pole end. 
The current, therefore, tends to increase 
the magnetism of the magnet and the 
lines of force of both are in the same 
direction. When the current is reversed, 
the tinsel unwinds and again twists 
magnet in a right-hand spiral, or so 
N is increased by the current's 



278 



PRACTICAL ELECTRICITY. 




Fig. 242.— Kotation of 
Current-Carrying Wire 
Around a Mag- 
netic Pole. 



267. Rotation of a Current-Carrying Wire Around a 
Magnetic Pole. — Since the tendency of a magnet is to urge a 
wire carrying a current to a position at right angles to it, con- 
tinuous rotation of the wire can be pro- 
duced if the wire be arranged free to 
move and in such a manner that it will 
never attain such a position. In Fig. 
242 a wooden ring with a groove turned 
in it for the reception of mercury is 
mounted above an electromagnet. One 
end of a piece of copper wire, AB, is 
hooked on to the stationary horizontal 
brass arm, which is supported by the 
vertical rod as depicted. The other 
end of the copper wire dips into the 
mercury trough and serves to complete 
the circuit of the batteiy current 
through the electromagnet. 

The magnetic field of the electro- 
magnet is nearly at right angles to the 
field of the wire, and the wire rotates 
about the pole, when the current is passed through it, accord- 
ing to the principle that a magnetic body free to move, tends to 
move so that its lines of force will 
be in the same direction as the lines 
of the field in which it is placed. 

The direction of rotation can 
be determined before the current 
is turned on by the following left- 
hand ride : 

Place the thumb, first and second 
fingers of the left hand all at right 
angles to each other, as in Fig. 2J/.3, 
and the hand so that the first finger 
indicates the direction of the lines 
of force of the magnet, and the second 
finger the direction of the current in 
the wire; the thumb will then in- 
dicate the direction of motion of the 
wire. Applying the left-hand rule to Fig. 242, we find that 
the wire will rotate in the direction opposite to the hands 
of the clock. It tends to wind around the pole in such 



Left Hand 




Fig. 243.— Left-Hand Rule for 

Determining the Direction of 

Rotation of a Moving AVire 

in a Magnetic Field. 
This rule applies to motors. 



ELECTR OD YNAMICS. 



279 



a direction as to increase the magnetism of the pole, just as 
in the automatic twisting experiment, *\\ 266. 

This rule is very convenient for determining the direction 
of rotation of motors, ^f 358. The moving wire in Fig. 242 
is analogous to the armature of the motor, and the electro- 
magnet, its field. 

If the direction of current through the armature and field of 
Fig. 242 be reversed, as by changing the binding post ter- 
minals, the direction of rotation will be the same as be- 
fore, because the current through the moving wire and the 
polarity of the field are both reversed, therefore, the same re- 
lation exists as before, which can be proved by the left-hand 
rule. If, now, only the current in the wire be reversed, or 
only the polarity of the field, then the direction of rotation 
is reversed, as proved by the left-hand rule. 

To reverse the direction of rotation of a motor, therefore, 
reverse the direction of current either through the armature or the 
field magnets, hut not through both. 

A permanent magnet can be substituted for the electro- 
magnet in Fig. 242, as the same principles are involved. 
The wooden ring could be 
lowered to the middle 
position of the magnet and 
the wire prolonged when a 
greater part of its field 
would be in the magnet's 
field. 

If the ring were located 
on the base, Fig. 242, and 
the wire, AB, extended the 
whole length of the magnet, 
one pole would tend to urge it in one direction and the other 
pole in the opposite direction, so that if the poles were of 
equal strength the wire would not rotate. 

Another device to produce continuous rotation is illus- 
trated in Fig. 244, and called Barlow's wheel. The edge 
of a pivoted copper disc dips into a trough of mercury located 
between the poles of a horseshoe magnet. The magnet's field 
acts at right angles to the current's field since the current 
flows from the periphery of the disc to its axis, and the disc 
rotates in the direction of the hands of a clock, Fig. 244, as 
can be determined by the left-hand rule. 




Fig. 244.— Barlow's Wheel. 
Faraday's disc dynamo driven as a motor. 



280 



PRACTICAL ELECTRICITY. 



268. Electrodynamics. — The term electrodynamics is ap- 
plied to the study of that part of electricity which treats of 
the force exerted by one current upon another. We have 
just noted the reciprocal action between a current and a mag- 
net, and now in electrodynamics, the mutual action of the 
currents upon each other is to be considered. Every wire 
through which a current is flowing is surrounded by a mag- 
netic field, and the magnetic fields of two wires react upon 
each other. This reaction may take place between two neigh- 
boring wires in the same circuit through which a current is 




Fig. 245. — Parallel Currents Flowing in the Same Direction Attract Each 
Other; if in Opposite Directions they Repel Each Other. 

flowing, or it may occur between wires in two independent 
circuits, the action depending on the relation between the 
two magnetic fields. 

269. The Magnetic Fields of Parallel Currents.— The 
magnetic field of a straight wire carrying a current was illus- 
trated in Fig. 128. If you regard magnetic lines as being of 
N-polarity when their direction is toward you, and of S-po- 
larity when their direction is away from you, then when the 
direction of the whirls is kept in mind, the N and S-polarity 
of a straight wire may be readily remembered. In the left- 
hand diagram of Fig. 245 the direction of the current, the 
direction of whirls and polarity of the wire are indicated. 
The wires pass through a piece of cardboard upon which, by 
the aid of iron filings, the graphical field is made. The cur- 



ELECTROD YNAMICS. 



281 



rent in the parallel wires flows in the opposite direction, so 
that the two adjacent sides are of the same polarity, thus 
causing a force of repulsion to exist between them. The 
wires tend to move away from each other. The field is very con- 
densed between the 
wires and elongated 
outside of them. 
Midway between the 
wires the lines of force 
are in the same direc- 
tion and fairly uni- 
form for a small area ; 
it is here that the 
needle of the tangent 
galvanometer is 
placed. (Compare 
with Fig. 139. ) The 
repulsion between the 
wires* may be demon- 
strated by the follow- 
ing experiment. 




Fig. 246. — Attraction and Repulsion Between 
Suspended Tinsel Wires Carrying Currents. 

A— Currents in the opposite direction— repulsion. 
B— Currents in %he same direction—attraction. 



Exp. 70: Support 
from a suitable stand a 
wire connector and suspend from ihe same two long, parallel, vertical 
pieces of tinsel wire arranged close to each other and connected to a 
source of current, A, Fig. 246. When the circuit is closed, the cur- 
rents being in opposite directions repel each other, and the wires 

move apart as depicted, accord- 
ing to the principles of fl 269. 

In the right-hand dia- 
gram, Fig. 245, the currents 
in the parallel wires are in 
the same direction and the 
polarities of the adjacent 
wires unlike, so that attrac- 
tion results according to the 
law for unlike polarities. 
This is noted in the filing 
diagram, where the field on 
the outside of the wires is 
very much condensed and 

247. — Attraction and Repulsion , J -. , , ., 

Between Parallel Currents. elongated between these 




282 



PRACTICAL ELECTRICITY. 




C A 

Fig. 248. — Attraction and Repul- 
sion Between Angular Currents. 



wires. There are also continuous curves embracing both 
wires, due to the unison of some of the magnetic lines of both 
wires. The wires tend to be drawn together by the tension 

along these lines of force. This 
attraction is demonstrated in 
Exp. 71. 

Exp. 71 : Pass the current through- 
the two parallel tinsel wires in B, Fig. 
246, in the same direction, and al- 
£ though the wires are separated for 
some distance they move toward 
each other, according to the principle 
in \ 269. 

270. Laws of Parallel and 
Angular Currents. — 1. Par- 
allel WIRES CARRYING CURRENTS 
AND FLOWING IN THE SAME DI- 
RECTION ATTRACT EACH OTHER; 
BUT IF THE CURRENTS ARE IN THE OPPOSITE DIRECTION THEY 

repel each other. See Fig. 247. This law is true for 
independent circuits or for two parts of the same circuit, 

2. TWO WIRES CROSSING EACH 
OTHER AT AN ANGLE ATTRACT 
EACH OTHER IF THE CURRENTS 
IN EACH OF THEM FLOW EITHER 
TOWARD TPIE POINT OF CROSS- 
ING OR AWAY FROM IT; BUT 
THEY REPEL EACH OTHER WHEN 
THE CURRENT FLOWS TOWARD 
IT IN ONE WIRE AND AWAY 
FROM IT IN THE OTHER. See 

Fig. 248 and Exp. 74. The 
motion tends to make the 
wires not only parallel, but ^ 
also coincident. This law is 
very important, and upon its 
principle are constructed elec- 
tro-dynamometers and watt 
meters, %% 272, 273, etc. 

3. The force between two parallel currents is propor- 
tional TO THE PRODUCT OF THE CURRENT STRENGTHS AND TO 
THE LENGTH OF THE WIRES CONSIDERED, AND VARIES INVERSELY 




Fig. 249.— The Movable Coil (AB) 
May be Attracted or Repelled 
by the Stationary Coil (CD) . 



ELECTR OD YNAMICS. 



283 



as the distance between them. The first and second 
laws may be further demonstrated by the ampere-frame coil 
described in ^[ 175. 

Exp. 72 : Connect the ampere-frame coil and rectangular coil in 
series, and to a source of current, Fig. 249. Trace the direction of 
current in each coil. Hold one side of the rectangular coil, CD, par- 
allel and close to one side of the movable coil, AB. The wire AB is 
repelled and moves away from CD when the currents are in opposite 
directions, Fig. 249. Invert the coil CD so that the current flows in 
the same direction through 

both, and the movable coil Si 

is attracted and will follow 
CD if it is carried around 
the axis of the coil AB. 

Exp. 73: Roget's Jump- 
ing Spiral.— A further proof 
of the first law is demon- 
strated by the following ap- 
paratus : a phosphor bronze 
spring is supported vertically 
by a stand, Fig. 250. The 
lower end dips into a cup 
of mercury, MC. Current is 
passed through the spring 
and flows around each con- 
volution in the same direc- 
tion, hence the magnetic 
fields of all the convolutions 
attract each other, and the 
length of the spiral is short- 
ened to such an extent that 
the lower end is pulled out 
of the mercury cup, thus 
breaking the circuit. Grav- 
ity now pulls the spring 
down again and the circuit 
is re-established, only to be 
broken by the same action. 
The spring thus vibrates con- 
tinuously like the vibrator of an electric bell. An iron rod lowered 
down through the centre of the spiral, so that it does not touch the 
convolutions, greatly increases the action by increasing the magnetic 
effects of the whirls around each wire. In any solenoid or electro- 
magnet, the magnetic field, therefore, tends to bind the wires closer 
together, as in Koget's spiral, since the current is in the same direc- 
tion through all the turns, and all the convolutions are parallel. 

271. Currents in Angular Conductors. — In Fig. 248 two 
insulated wires AB and CD make an angle with each other, 
and the currents flow from A and C toward P, and the por- 




Jumping Spiral. 



It illustrates the law of parallel currents flowing 
in the same direction. 



284 



PRACTICAL ELECTRICITY. 



tions AP and CP attract each other, according to Law 2. This 
is indicated by the polarity of the wires and the direction of 
the whirls around them. 

Currents also flow away from P, toward B and D, and simi- 
lar attraction takes place according to Law 2. Now consider 
the current and polarity in the part of the wire AP and PD. 
In AP the current flows toward P, and in PD away from P, 
and repulsion exists as indicated. This law can be experi- 
mentally demonstrated by the apparatus described in Exp. 
74. 

Exp. 74 : Inside of the movable rectangular coil AB, Fig. 251, is 
clamped a fixed coil CD. The two coils may be connected in series 
or to two independent circuits. The movable coil, AB, is turned so 
that its plane makes an angle with the plane of the coil, CD. If the 
current be sent through the coils so that it flows along AB and CD 
either toward or away from their angle of intersection, the coil, AB, 
will move in the direction of the arrows till its plane ' coincides with 

that of CD, or till they are parallel, 
according to Law 2. If, now, the 
current through either but not both 
of them be reversed, the coil, AB, 
will move against the direction of 
the arrows and complete one-half 
revolution, till its plane coincides 
w T ith CD, when B will be directly 
above C. This motion is in accord- 
ance with the latter half of Law 2, 
when the currents flow in one wire 
toward the point of crossing, and 
in the other wire away from it. 

272. The Electro-Dyna- 
mometer. — The electro-dyna- 
mometer is an instrument for 
measuring current strength by 
the reaction between two coils, 
one of which is fixed and the 
other movable, and through which the current to be measured 
is passed. The general appearance of the laboratory type, 
known as a Siemens dynamometer, is illustrated in Fig. 252, 
and the diagram of the circuits is shown in Fig. 253. The fixed 
coil, CD, containing a number of turns of wire is fastened to 
a vertical support. The movable coil, AB, of a very few turns 
of wire, is large enough to embrace the fixed coil when their 
planes are at right angles to each other, and is suspended by 
a strong piece of thread below the cardboard dial. The ends 




Fig. 251. — Angular Currents Tend to 

Become Parallel and Flow in 

the Same Direction. 



ELECTR OD YNAMICS. 



285 



of this coil, being free to move, dip into two cups of mercury, 
located one above the other along the axis of the coil. Con- 
nections are made as indicated, so that the two coils are in 
series when connected to an external circuit. The planes of 
the coils should be at right angles to each other. When the 
current flows through both coils, the movable coil tends to 
turn, according to Law 2 for angular currents. 

The force measured is the force which must be applied to 
keep the movable coil at right angles against the turning effort 





Fig. 252. — Siemens Dynamometer. 
Laboratory pattern. 



Fig. 253. — Connections 
of Siemens Dyna- 
mometer. 



due to the current. One end of a spring, S, is rigidly fastened 
to the movable coil, and the other end terminates in a mill- 
headed screw on the face of the dial, which can be turned so 
as to apply torsion to the spring. The movable coil carries 
an index pointer bent at right angles, which swings between 
two stop pins on the dial and rests directly over a fixed zero 
line when the coils are at right angles. To the torsion screw 
is attached a pointer which sweeps over a degree scale. When 
the movable coil is deflected against a stop pin the torsion 
screw is rotated in a direction to oppose the current's action, 



286 



PRACTICAL ELECTRICITY. 



and when the- coil is brought back to its original position the 
number of degrees through which the torsion pointer was 
turned, is noted. 

The current is directly proportional to the square root of 
the angle of torsion. For example, if with one current the 
number of degrees noted was 36 and with another current, 144, 
then the currents are to each other as the square roots of 36 
and 144, or as 6 is to 12, or one current is twice as strong as 
the other. To determine the current in amperes, the square 
root of the angle of torsion is multiplied by a constant found 
by calculation and furnished by the makers. The Siemens 
dynamometer is an accurate instrument connected in cir- 
cuit like an ammeter and 
has the advantage of being 
adapted for use with either 
direct or alternating cur- 
rents. 

273. Portable Dyna- 
mometer Ammeter. — A 
portable commercial form of 
electrodynamometer for use 
as an alternating or direct 
current ammeter is illus- 
trated in Fig. 254. The 
operation and principles in- 
volved are substantially the 
same as those given for 
the Siemens dynamometer, 
% 272, but the scale is 
amperes. When used on 
accurate results are obtained 
of two readings made with 
fixed coil is divided into two 




Fig. 254. — Dynamometer Ammeter for 

Alternating or Direct Currents. 

Portable Form. 



graduated to read directly in 
a direct current circuit more 
by taking tne average value 
the current reversed. The 
coils wound with a different number of turns, each of which 
is inserted in series with the movable coil and brought out to 
separate posts. Thus, if it is desired to measure a current 
known to be between one-tenth and 1 ampere, the right-hand 
binding posts are used, and if between 1 and 100 amperes, 
the left-hand posts are used, This arrangement produces a 
double scale instrument whereby a small current can be meas- 
ured with much greater accuracy. 
274. Dynamometer Wattmeter. — The energy in watts 



ELECTRO D YNAMICS. 



287 



expended in a circuit is equal to the product of the volts, E, 
and the current C, or W = E X C, Formula (62). These 
factors may be determined by 
a volt and an ammeter and 
multiplied together, or the 
multiplication may be auto- 
matically performed by using 
a form of Siemens dynamom- 
eter which measures the watts 
directly, and is, therefore called 
an indicating wattmeter. Sie- 
mens dynamometer wattmeter 
operates upon the same prin- 
ciples as the dynamometer 
ammeter, ^[ 272, but the two 
coils are not connected in series. 
The stationary coil, or the am- 
pere coil, is connected in series 
with the line like an ammeter, 
Fig. 255, and is wound with a 
few turns of heavy ivire having 
a low resistance. These termi- 




Fig. 255.— Connections of a Dyna- 
mometer Indicating Wattmeter. 



nals are brought out to two binding posts, as shown at the left 
of the Weston direct reading portable wattmeter, Fig. 256. The 
movable coil, or volt coil, is wound with a few turns of very fine 

ivire and connected in 
series with a high resist- 
ance, the terminals be- 
ing brought out to in- 
dependent binding 
posts, as shown at the 
top of the Weston in- 
strument. A push 
button switch is in- 
serted in the volt coil 
circuit. The mov- 
able coil thus cor- 
responds to the volt- 
meter and is con- 
nected to any circuit 
in the same manner 
Fig. 256.— Weston Direct Beading Wattmeter. as a voltmeter. 




288 PRACTICAL ELECTRICITY. 

The current in the volt coil will vary as the potential dif- 
ference between its terminals and the current through the 
ampere coil will vary as the current in the circuit in which 
it is inserted. The force acting upon the movable coil, or the 
force required to bring it to zero, depends on the current 
through both coils, or directly upon the watts expended in 
them. In the Weston portable instrument the movable coil 
is constructed and mounted similar to the coil shown in 
Fig. 198. The movable coil turns against the torsion of the 
spring and its pointer swings over a scale graduated in watts. 
The instrument is, therefore, direct reading, as in the case of 
a voltmeter. In Fig. 255 the proper connections of the in- 
strument for measuring the watts consumed by the incan- 
descent lamps are shown. The pointer indicates the watt 
consumption by the lamps. (Compare with Fig. 214.) 
. The Weston instrument requires no adjustment to secure 
a balance of the forces acting, and so momentary fluctuations 
are readily noted on the scale. This instrument can be used 
on any circuit and is rated according to the carrying capacit}' 
of the ampere coil and the potential to be applied across the 
volt coil. For example, in a 1500-watt instrument the maxi- 
mum current is 10 amperes and the maximum voltage 150 
volts. The capacity of the volt coil can be increased to any 
desired range by the use of a portable box of extra re- 
sistances, called a multiplier, connected in series with it. 

275. Thomson Recording Wattmeter. — The Weston in- 
dicating wattmeter, ^[ 274, gives the instantaneous values of 
the watts expended in a circuit, just as a voltmeter indicates 
the fluctuations in volts. To find the watt-hours consump- 
tion of electrical energy by such a meter, it will be neces- 
sary to multiply the average of a number of readings taken 
during a given time, by that time, expressed in hours, \\ 223. 
As the name implies, the readings of a Thomson recording 
wattmeter, give the total watt-hours consumption of energy, 
or it automatically multiplies the average of the instantane- 
ous indications by the time. It is, more correctly speaking, 
therefore, a joulemeter, ^f 217. Its principle of operation is 
that of the Siemens dynamometer, % 272, but, the movable 
coil rotates. The method of producing this rotation may be 
demonstrated as follows : 

In Fig. 251 continuous rotation of the coil, AB, around the coil, 
CD, could be produced, if at each instant the coil, AB, became par- 



ELECTR OD YNAMICS. 



289 



allel to CD, the current were automatically reversed through it. With 
the single turn and a strong current, sufficient repulsive impulse 
would be produced to move it through 180° : if the current be 
now reversed it will receive a similar repulsive impulse and 
will be repelled through another 180°, and so on. There 
will thus be two reversals and two impulses given to the 
movable coil each revolution, and continuous rotation produced. 
The force producing the rotation will still be dependent upon 
the current in both coils ae in the dynamometer. A uniform 
force for producing rotation would require several coils similar 
to AB and arranged about a vertical axis, with their planes at 
angles to each other, so that as one coil moved away from the station- 
ary coil another would take its place. Such an arrangement would 
be practically a motor, 
the moving coils form- 
ing the armature and 
the stationary coil the 
field. A worm on the 
armature shaft engag- 
ing with the train of 
wheels of a cyclometer 
dial would record the 
speed, and since the 
number of revolutions 
in an hour depends on 
the current through 
the coils during that 
time the cyclometer 
dial could be cali- 
brated in watt-hours, 
provided the speed 
were proportional to 
the energy supplied. 

The Thomson re- 
cording wattmeter 
is a simple type of 
motor, driven by 
the same electrical g * 
energy which it is to 
measure ; its rotation during any period is proportional to the 
power in watts delivered to the circuit during that time. The 
movable coil or armature revolves between two stationary coils 
with its axis at right angles to the axes of these coils, as shown 
in Fig. 257, where the meter cover is removed. The mova- 
ble coil, Fig. 258, is a drum-wound armature, ^| 328, without 
an iron core, and the current through its coils is reversed 
automatically by the commutator, 51 323, thus causing it to 
revolve. Current is led to the commutator by the wiping 
19 




257. — Thomson Recording 
Case Eemovec 



Wattmeter with. 



290 



PRACTICAL ELECTRICITY. 



contacts or brushes, B. A worm, S, on the upper end of the 
armature shaft engages a set of wheels which records the watt- 
hours on a dial. The armature is very light and delicately 
poised between jewel centres, so that the friction is reduced to 
a minimum here as well as in the train of wheels. 

To the lower end of its shaft is rigidly fixed, at right angles, a 
copper disc which rotates with it in the magnetic field of three 

permanent stationary- 
steel horseshoe magnets. 
The N -poles of these 
magnets are above and 
the S-poles below the 
copper disc, and it cuts 
the magnetic lines of 
force as it revolves. Eddy 
currents, ^[ 292, are in- 
duced in the copper disc, 
and the reaction of their 
magnetic field tends to 
retard the rotation. The 
amount of this retarding 
effect is directly propor- 
tional to the speed of 
rotation. Since the 
angular force causing the 
armature to rotate is di- 
rectly proportional to the 
magnetic field of the cur- 
rents in the two coils, 
and the retarding angular 
force also proportional to 
the magnetic field set up, 
the armature must rotate 
at such a speed that the 
electromagnetic driving 
torque is exactly equal 
to the electromagnetic 
retarding torque. Then with a constant pressure maintained 
in the wattmeter coils for any length of time, the number of 
revolutions of the armature, and therefore the travel of the dial 
hands will also be constant during the time, and proportional 
to the energy supplied. 




. 258. — Drum- Wound Armature of 
'homson Recording Wattmeter. 



ELECT R OD YNA MICS. 



291 




Shunt. 



A high resistance is inserted in series with the armature and 
it is connected to a circuit just like the volt coil of the indi- 
cating wattmeter in Fig. 255. The stationary current coils 
are wound in the same direction to produce the field, and are 
connected in series with the circuit, 
as in Fig. 259. The meter dials are 
graduated in watt-hours and read 
like a gas meter. The speed of the 
motor is materially reduced by the 
drag produced by the copper disc so 
that the dial reading is multiplied by 
a constant, the value of which is 
given on the dial ; a constant of 6, 
therefore, means that the meter dial [|- 
has recorded only 1-6 of the energy 
and its indication must be multiplied 
by 6 to obtain the true watt-hour 
consumption. The constant is used 
to avoid a high speed of rotation. 
Thomson wattmeters can be used on 
alternating or direct current circuits, 
and are made in different sizes 
according to the current carrying 
capacity of the ampere coil. The amount of extra resistance 
in the armature circuit depends on the voltage to which it is 
to be subjected. These meters are extensively used on com- 
mercial motor circuits and in individual house electric light 
service, similar to a gas meter, and are sensitive enough to 
record the energy through even one lamp when connected to 
the supply circuit. 

QUESTIONS. 

1. Two parallel wires are stretched from vertical supports, the 
measured distance between them being 2 inches. A current is sent 
through the wires, and the distance is now only If inches. How do 
you explain this? 

2. What is the direction of the current in the wires in question 1 ? 

3. The current is reversed in both wires in question 1. How will 
they now be affected ? 

4. Make a complete sketch of a Thomson recording wattmeter 
connected between the two street mains, entering a consumer's build- 
ing, and the parallel lamp circuit. 

5. A Siemens dynamometer is connected in series with some in- 
candescent lamps, and the torsion head must be turned through 121° 



Fig. 259. — Connections of 
Thomson Recording 
Wattmeter. 



292 PRACTICAL ELECTRICITY. 

to bring the movable coil to zero position. Some lamps are now- 
turned off and the angle corresponding with the zero position is 81°. 
The constant of the instrument is 2. What is the strength of cur- 
rent in each case ? Ans. 22 ; 18 amperes. 

6. Make sketch in detail of a Weston indicating w r attmeter con- 
nected to a motor circuit so as to indicate the power being absorbed. 

7. Two wires cross each other at an angle of 60° and the current 
flows through them in an opposite direction. Will they tend to 
move so as to increase or decrease the angle of crossing? 

8. What is the advantage of a djmamometer ammeter over one 
constructed upon the D'Arsonval principle? 

9. Explain the difference between an indicating and recording 
wattmeter, stating the principles involved in each. 

10. A vertical wire carrying a current rotates around the S-pole of 
a magnet in a direction against the hands of a clock as viewed from 
the S-pole end. Ts the current flowing up or down the wire? 

11. A copper disc is mounted between the poles of a horseshoe 
magnet and current passed from its centre to the circumference. 
Make a sketch indicating the direction in which the disc will rotate. 

12. How can you change the direction of rotation of the disc in 
question 11? 

13. Make complete sketch of connections of a double scale dyna- 
mometer ammeter. 

14. Current is passed downward through a vertical wire, and a bar 
magnet with its N-pole held uppermost is placed near to and parallel 
with the wire. Suppose the magnet to be flexible, like a piece of 
tinsel, what will occur ? Make sketch. 



LESSON XXIV. 

ELECTROMAGNETIC INDUCTION. 

Electromagnetic Induction — Currents Induced by a Magnet in a 
Wire — To Find the Direction of the Induced Current (Fleming's 
Eight-hand Rule) — Upon What Factors the Value of the Induced 
E. M. F. Depends — Currents Induced in a Coil by Motion of a 
Magnet — Primary and Secondary Coils — Lenz's Law of Induced 
Currents— Classification of Induction Currents — Currents In- 
duced by Electromagnetism — Five Methods of Producing In- 
duced Currents— Table of Induction Currents — A 7 ariation of 
Induced E. M. F., with the Rate of Change of Magnetic Lines 
of Force (Faraday's Law) — Eddy Currents (Arago's Rotations) — 
Mutual Induction— Self-Induction — Gas Lighting Spark Coil — In- 
ductance—Reactance and Impedance — Choke Coils — Neutralizing 
the Effects of Self-induction — Questions and Problems. 

276. Electromagnetic Induction. — In Lesson XV a cur- 
rent of electricity flowing through a wire was found to set 
up around the wire a magnetic field, Fig. 129. The mag- 
netic field was maintained around the wire at the expense of 
chemicals inside the cell. If a wire be arranged so as to form 
a closed circuit and then moved across a magnetic field, a 
current of electricity is produced in the wire ; in other words, 
if we artificially produce around the wire the magnetic 
whirls, a current of electricity flows through it when the 
circuit is complete. The English physicist, Michael Fara- 
day, discovered (in 1831) that electric currents could be in- 
duced in a closed circuit by moving magnets near it, or by 
moving the circuit across a magnetic field. Currents that 
are so generated are known as induction currents and the 
phenomenon termed electromagnetic induction. (Compare with 
magnetic induction, ^| 36.) This is a most interesting and 
valuable branch of the study of electricity, as upon its prin- 
ciples is based the operation of many forms of commercial 
electrical apparatus, such as dynamos, transformers or in- 
duction coils, telephones, etc. 

277. Currents Induced in a Wire by a Magnet. — A 
sensitive galvanometer, G, Fig. 260, is removed from the in- 

293 



294 



PRACTICAL ELECTRICITY. 



~~\> 




Fig. 260. — Current Induced in 

a Wire by Moving it 

Past a Magnet. 



fluence of the bar magnet, NS, and connected by a piece 
of copper wire. If a portion of the wire, AB, is quickly 
moved down past the pole of the magnet a momentary current is 
induced in the wire, causing the galvanometer needle to be 
deflected, say to the right of zero, when it will again return to 
,«:».«:.■.. the zero position. If the ■ wire is 

again moved up past the same pole 
another momentary current is in- 
duced in the wire in the opposite 
direction to the former current, as 
indicated by the momentary deflection 
of the galvanometer needle, which 
now swings to the left of zero. If 
the induced current, then, flows from 
A to B on the downward motion it 
will flow from B to A on the upward 
motion. If the wire be moved 
rapidly up and down past the mag- 
net, the current will alternate in 
direction with each direction of 
motion, or an alternating current, 
^j 320, will be induced in the wire. When this motion is 
rapid, and consequently the alternations, the needle does 
not have sufficient time to take up the respective positions 
due to the opposite currents flowing around it, and, there- 
fore, remains at zero, appreciably vibrating, however. The 
induced current is constant, but alternating in direction. 

(1.) If the wire is held stationary and the magnet moved, the 
same results are noted. 

(2. ) If the opposite pole is used, the direction of the current in 
each instance is opposite to what it was before. 

(3.) An electromagnet used instead of the permanent bar mag- 
net will produce the same residts. 

(4. ) The induced current does not weaken the magnet, but is 
produced by the expenditure of muscular energy, just as in a cell 
the current is produced by the expenditure of chemical energy. 

(5.) The momentary induced current is greatest when the wire 
is moved so as to cut the magnetic lines of force at right angles. 

(6. ) The direction of current in the wire is at right angles to the 
direction of the lines of force of the magnet. 

(7.) Current in any wire depends upon the E. M. F. causing it 
to flow, so that properly speaking, an E. M. F. is induced in the 



ELECTR OMA GNETIC IND UCTION. 



295 



Right Hanl 




wire when it is made to cut magnetic lines of force, and a current 

floivs ivhen the circuit is complete, due to this induced E. M. F. 
(8.) If the wire is cut at any point, in Fig. 260, an E. M. F. 

is maintained at the terminals of the wire, when motion occurs, just 

as an E. M. F. exists at the terminals of a cell on open circuit 

tending to cause a current to flow, ^| 70. 
278. To Find the Direction of the Induced Current. — 

Fleming's Right-Hand Rule. — Place the thumb, the first 

and second fingers of the right hand 

all at right angles to each other, Fig. 

261, and in such relation to the wire 

that the first finger points in the 

direction of the lines of Force of the 

magnet, and the thumb, in the 

direction of motion; the Second 

finger will then indicate the direc- 
tion OF THE induced current. 
Applying this rule to the wire, 

AB, Fig. 262, which is being 

moved down past the N-pole of 

the magnet we find that the 

direction of current is from B 

toivard A. If either the polarity 

or direction of motion be reversed, the current in the wire AB 

will be reversed, as can be proved by this rule. If both the 

polarity and motion are reversed the current is in the same 

direction as in the figure. The 
student should prove these 
statements by the above rule. 

Another method of ascertaining 
the direction of the induced current 
is to keep in mind the direction of 
the magnetic whirls around the 
wire, corresponding to the direc- 
tion of current through it as you 
look along the wire, Fig. 136. If 
you look along the wire from A 
toivard B, Fig. 262, while it is being moved downward across the lines 
of force, the direction of these lines underneath the wire is from left 
to right, and the direction of motion such that if the magnetic lines 
'were flexible they would be wrapped around the conductor in a direc- 
tion opposed to the motion of the hands of a clock. Since the tendency of 
the induction is, in this case, to produce magnetic whirls, the direction 
of which is anti-clockwise as you look along the wire, the current set up 
flows toward you, or from B toward A. (Compare with Fig. 130. ) 



Fig. 261.— Eight-Hand Rule for 

Determining the Direction 

of Induced Current — 

Fleming's Rule. 




MOTJOM 



Fig. 262. 



-Application of Fleming's 
Rule. 



296 



PRACTICAL ELECTRICITY. 



mi 



Fig. 263.— Increasing the In 
duced E. M. F. by Increas- 
ing the Number of 
Cutting Wires. 



279. Upon What Factors the Value of the Induced E. 
M. F. Depends.— 

(1.) If the wire AB, Fig. 260, be moved very rapidly past 
the pole of the magnet, the momentary induced E. M. F. , and 
pm&£-:-\; therefore the current is greater than 

when it was moved more slowly, as 
indicated by the magnitude of the^ 
needle's deflection. 

(2.) If a stronger bar magnet, as 
two similar magnets with like poles 
together be used, the induced E.M. F. 
will be greater than when only one 
magnet is used, as will be indicated 
by the galvanometer needle. The 
rate of motion should be the same 
in each case. 

(3.) If more than one wire be 
made to cut the magnetic field, Fig. 
263, a greater E. M. F. will be in- 
duced than when only one wire or 
turn is moved past the pole at the same speed. This will be 
indicated by the greater momentary deflection of the galva- 
nometer needle. From the above statements, then, the 
induced electromotive force is dependent upon, and it can 
also be proved to be pro- cmo/m* 

portional to, Jl «« 

(a) The number of mag- 
netic lines of force cut, or 
the strength of the field; 

(6) The speed or rate 
at which the lines of force 
are cut ; 

( c ) The number of wires 
cutting the lines of force. 

280. Currents In- 
duced in a Coil by- 
Motion of a Magnet.— 
Instead of moving the 
Fig. 260, the wire may 
Figs. 264 and 266, and 



of Magnet 
/ 




Fig. 264.— The Polarity of the Induced 

Current Tends to Stop the Motion 

Producing It— Lenz's Law. 



wire down past the magnet m 
be coiled up, as in the solenoid, 
connected to the galvanometer. 
If now either a permanent or an electromagnet be thrust 
into the solenoid, a momentary induced current will flow 



ELECTR DMA GNETIC IND UCTION. 297 

around the galvanometer according to the conditions given 

in % 277. 

Exp. 75 : Connect the student's galvanometer, Fig. 153, to the 
secondary coil, Fig. 266, and using the bar magnet set, Fig. 13, make 
experiments to verify all the statements given in % 277. 

Exp. 76 : With the same apparatus as in Exp. 75, prove statements 
(a) and (b) in ^[279. Using one magnet, the momentary deflections 
of the needle will be about 25 for an average thrust. 

Exp. 77 : To prove statement (c), % 279, substitute for the secondary 
coil used in Exp. 75 the solenoid depicted in Fig. 145, which contains 
a different number of turns of wire. 

Exp. 78: Connect a cell to the detector galvanometer, Fig-. 153, 
and note whether the needle is deflected to the right or left of zero 
when the current enters by the right-hand binding post. Having 
determined the direction of deflection for a particular direction of cur- 
rent through the instrument, substitute for the cell the secondary 
coil, and repeat the experiments enumerated in ^ 277. Find the 
direction of the induced current in the coil by tracing the direction 
of the winding, noting, the direction of deflection of the galvanometer 
needle and using Fleming's right-hand rule, ][278. Make note-book 
sketches. 

281. Primary and Secondary Coils. — The word primary 
is often used as an abbreviation for primary coil. The primary 
coil is the coil producing the induction, or it is the inducing 
body, while the secondary coil, or secondary, is the body under 
induction. In Fig. 264 the bar magnet is the primary body 
and the coil, the secondary body. In Fig. 266 an electro- 
magnet is substituted for the bar magnet, and is called the 
primary coil. 

282. Lenz's Law of Induced Currents. — If Exp. 78 be 
carefully performed it will be found that, as the N-pole of a 
magnet is thrust toward the coil, the direction of the induced 
current will be such as to make the face of the coil near to 
the magnet's pole of the same polarity as that pole, Fig. 264 ; 
hence, there is a magnetic repulsion between the magnet and the 
coil when one is being approached to the other. When the mag- 
net's pole is withdrawn the direction of the induced current is 
reversed ; the face near the magnet has now, therefore, opposite 
polarity to the pole of the magnet, and consequently attraction 
exists between them. In each instance the magnetic attractions 
or repulsions tend to oppose the motion of the magnet. The above 
statements are expressed concisely in Lenz' s Law, as follows : 

In all Cases of Electromagnetic Induction the Direc- 
tion of the Induced Current is Such as to Tend to Stop 
the Motion Producing It. To produce the induced current 



298 



PRACTICAL ELECTRICITY. 



energy must be expended in bringing the magnet to the 
coil and in taking it away. If the magnet is made to 
approach by hand, muscular energy is expended ; if attached 
to the end of the piston rod of a steam engine and moved in 
and out of the coil, mechanical energy is expended and a 
constant but alternating current produced. It will also be 
seen that if the coil terminals are open or disconnected very 
little energy will be required to move the magnet, since there 
will now be no attractions and repulsions to overcome. 

The extra energy required when the coil is closed is ex- 
pended in producing the induced current, and it is in this 
way that mechanical energy is converted into electrical energy in 
the dynamo. It will be further noted that with a given rate 
of motion the alternating E. M. F. will be constant, and, 

since the resistance of the 
A WW*™ c0 ii is instant, the cur- 
rent will also be constant. 
Suppose a galvanometer 
of much lower resistance 
is connected to the coil, 
Fig. 264. The current 
will now be greater, since 
the resistance is de- 
creased, and, conse- 
quently, the watts will 
be greater, W = E X C, 
so that more energy must 
be expended in produc- 
ing the E. M. F. than before, because the magnetic field of the 
coil to be overcome has been increased by the increase of cur- 
rent strength. When lamps are added in parcdlel to the circuit 
of a dynamo the resistance of the circuit is lowered^ Formula (43), 
therefore the E. M. F. causes more current to flow through the lower 
resistance and more mechanical energy must be expended in pro- 
portion to the additional electrical energy furnished. 

Lenz's Law is further illustrated in Fig. 265, where the 
primary body, A, is an electromagnet with its polarity as in- 
dicated. On moving this electromagnet toward the secondary 
coil, B, the induced current flows so as to make the near face 
of B of N-polarity, and repulsion results as before. During 
the recession of the primary from the secondary coil the polar- 
ity of the secondary is reversed and attraction exists, opposing 




Fig 265.— The Polarity of the Induced Cur- 
rent Tends to Stop the Motion 
Producing It. — Lenz's Law. 



ELECTROMAGNETIC INDUCTION. 



299 



their separation. The attractions and repulsions take place 
only while the coil is moving. If the coil stops the induced 
current in the secondary also stops, even though the current 
still flows in the primary coil. See also ^| 292. 

283. Classification of Induction Currents. — Induction 
is produced whenever a conductor is cut by magnetic lines 
of force, no matter how this cutting may be accomplished. 
The induction resulting from different combinations of mov- 
ing magnetic fields and conductors may be classified as follows : 

(a) Magneto- electric induction, 

(b) Electromagnetic induction, 

(c) Mutual induction, 

(d) Self-induction. 

In magneto-electric induction a permanent magnet is used to 
produce the magnetic field, and either the wire or the field 
may be moved to produce induction. 

In electromagnetic induction the magnetic field of a current 
or an electromagnet is utilized to produce the induction. 
Mutual induction and self-induction are 
defined in ^f^[ 293 and 294 respectively. 

284. Currents Induced by Electro- 
magnetism. — Momentary induction 
may be produced in the secondary circuit 
of the student's induction coil, Fig. 266, 
by any of the following methods : 

1. By moving either the primary or 
secondary circuit. 

When both coils are stationary and 
one surrounds the other : 

2. By making or breaking the primary 
circuit. 

3. By altering the strength of the current 
in the primary circuit. 

4. By rapidly reversing the direction of 
the current in the primary circuit. 

5. By moving the iron core when a current 
is flowing through the primary circuit. 

A momentary induced current which flows in the opposite 
direction to that of the current producing it, is defined as an 
inverse current, and one which flows in the same direction, a 
direct current. The above methods for producing induction 
are treated in the following paragraphs. 




Fig. 266.— Student's Ex- 
perimental Induc- 
tion Coil. 



300 



PRACTICAL ELECTRICITY. 




Fig. 267.— The Magnetic Field 

of the Primary (CD) Cuts 

the Secondary (AB). 



A simple form of student's induction coil is illustrated in Fig. 266. 
The primary is a wooden spool wound with 2 layers of No. 15 B. & 
S. insulated copper wire, with the terminals securely fastened to 

binding posts, which are mounted at 

right angles to the coil. The latter is 

drilled to permit free movement of a 

— \ three-eighth inch soft iron core to which 

£__y B is attached a brass eye bolt. Eesistance 

of primary is about .07 ohm. Six layers, 

D of No. 30 B. & S. wire are wound on the 

secondary coil, which has a resistance of 

about 20 ohms. 



285. First Method.— Moving 
Either the Primary or Secondary Cir- 
cuit — When either the primary or 
secondary circuit is moved relatively 
to the other the results are the same as those given for a per- 
manent magnet in ^[ 277, and should be verified by the 
apparatus shown in Fig. 266. The principle involved may 
be further explained as follows : 

consider the switch closed in the ^ <( \ 

primary circuit, CD, of Fig. 267 ; 
magnetic whirls surround the wire 
as in Fig. 129. Now move the' 
secondary wire, AB, toward CD, and^ff ~ 
it is cut by the lines of force of the |l|^ 
primary circuit, producing a mo- 
mentary current during the motion. Fig. 268. 
The direction of this induced cur- 
rent is opposed to that of the primary current as indicated, 
Fig. 268, and it is an inverse current. If the secondary be 
moved away from the primary, Fig. 269, the secondary cir- 
^^^ cuit is again cut by the primary, 

\ty 1 an( ^ a direct momentary current 

Tmotjojv is induced. 

286. Second Method.— Mak- 
ing or Breaking the Primary Cir- 
cuit. — Consider both circuits 
stationary in Fig. 267. At the 
instant the switch is closed the 
magnetic lines of force springing 




tJ 

-Inverse Induced 
Secondary Current. 



A.K 



c[= iS 



Fig. 269.— Direct Induced 
Secondary Current. 



from the primary, CD, cut the secondary circuit, AB, and 
an inverse* momentary current flows through the secondary, 
left-hand diagram, Fig. 270, for the period of time required 



ELECTR OMA GNETIC IND UCTION. 



301 



to establish the electromagnetic field around the primary, 
% 315. When the switch is opened the magnetic lines 
of the primary will collapse upon it and again cut the 
secondary, but in the opposite direction, producing a direct 




Fig. 270. — Inverse Induced Current on "Make" of Circuit, Direct 
Current on "Break." 

current, right-hand diagram, Fig. 270. If the primary 
switch be automatically closed and opened a great many 
times per second, the momentary induced currents will be- 
come constant in duration, but will change their direction with 
,p 
s 



Primary Coil 





Fig. 271. — Direction of Momentary Induced Currents in the 
Secondary Circuit. 

each make and break of the primary. Whether the circuits 
are wound in flat spirals or in cylindrical coils, Fig. 271, the 
same principles apply. The induction coil, •([ 300, is con- 
structed on this principle. 

287. Third Method.— Altering the Strength of the Pri- 




302 PRACTICAL ELECTRICITY. 

mary Current. — If a rheostat be introduced into the primary 
circuit the current can be altered without breaking the cir- 
cuit, Fig. 272. When the resistance is decreased a momentary 
inverse current is induced in the secondary circuit, since the 
magnetic lines of the primary at the instant of change in re- 
sistance are greater than before, or spring outward.' With an 
increase in resistance the primary lines cut the secondary in 
the opposite direction as they collapse toward the primary wire, 
and a direct momentary current is induced. 

288. Fourth Method.— Reversing the Direction of the Pri- 
mary Current. — A switch arranged to automatically reverse 
the primary current many times per second would produce 
an alternating current, the magnetic whirls of which would be 
continually rising, falling, and changing their direction with 

each reversal. A secondary wire brought 
into the vicinity of a wire carrying such 
a current would be continually cut by 
its magnetic lines of force, and a constant 
induced alternating current obtained, the 
> variations of which would be like those 

L_Ji|i_yJ |J in the primary circuit. When an electro- 

ifi IP * magnet is supplied with an alternating 

Fig.272.-Momentary current, the polarity reverses with each 
Induced Currents by reversal oi current so that the magnet s 
Varying strength of field is continually in motion, and will 

Primary Current. , -> . . • , ■ • • , rn. 

cut any conductor in its vicinity. I he 
alternating current transformer is dependent on this principle 
and an alternating current dynamo, ^f 320, generates a current 
of this character. 

289. Fifth Method. — Moving the Iron Core. — If a piece of 
iron be so moved, relatively to the primary and secondary 
circuits, that it increases the magnetic lines of force of the 
primary wire, an inverse current is induced in the secondary, 
lasting only while the increase takes place. When moved so 
as to produce a decrease of primary lines a direct induced 
current results. This principle is used in an inductor type of 
an alternating current generator. The induction is produced 
by rotating iron poles between the stationary primary and 

x secondary circuits. 

290.— Table of Induction Currents. — The character and 
methods of producing induced currents are summarized as 
follows : 



ELECTROMAGNETIC INDUCTION. 
Table XVIII.— Induction Currents. 



303 



By means of 



Magnet . 
Current. 



Momentary Inverse currents 
are induced in secondary 
circuit. 



While approaching. 

While approaching or 
beginning or increas- 
ing in strength. 



Momentary Direct currents 
are induced in secondary 
circuit. 



While receding. 

While receding or end- 
ing or decreasing in 
strength. 



Exp. 79 : With the student's induction coil, Fig. 266, all of the 
above cases should be verified and the results noted. To ascertain 
whether the induced current is a direct or inverse one the relation 
between the galvanometer deflection and the current should be 
determined, as in Exp. 78. 

291. Variation of Induced E. M. F. with the Rate of 
Change of Magnetic Lines of Force. — Faraday's Law. — To 
produce induction in a closed coil located in a magnetic field 
it must be so moved that the number of lines of force thread- 
ing through it are constantly changing. 

The induced E. M. F. is proportional to the rate of change of the 
magnetic lines threading through the coil. For example, take the 
closed coil of wire, A, Fig. 273, located in a uniform magnetic 




Fig. 273.— No Induced Current in a Loop When Moved so That There is No 
Rate of Change of the Magnetic Lines Through It. 

field, NS, with its plane at right angles to the lines of force. 
When the coil is moved vertically downward across the field 
to position B, magnetic lines of force are cut, but no induc- 
tion results since the number of lines of force threading 
through the coil have not been altered. 

From another standpoint the upper half of the coil cuts 
the lines in the same direction as the lower half, consequently 
the direction of the induced E. M. F. in each half is the same, 
or the E. M. F.'s are opposed to each other, and, being of the 
same value, no current can flow. If the coil A be held either 



304 PRACTICAL ELECTRICITY. 

in a vertical position or at an angle, and then moved across 
the field in the direction of the arrows to either position, I) or 
C, no induction will take place for the same reasons. If the 
coil be now turned through any angle to its vertical position, 
say 45°, as shown in position B, Fig. 274, the number of 
lines of force threading through it are altered (decreased), 
and during the angular motion an induced current flows 
around the ring in the direction of the arrow. In this case 
each half of the coil cuts the lines of force in an opposite 
direction, consequently the induced E. M. F.'s are also oppo- 
site in direction and in series with each other. The current, 
therefore, flows around the ring. 

When moved through the next 45°, or from B to C, the 
rate of change of magnetic lines through the coil continues, 
and is greater than when it is moved from A to B. This will 
be seen by noting the comparative number of lines above 
coil B, which pass over it instead of threading through it at 




160° 



Fig. 274.— Phases of Induction in a Closed Loop When Rotated in a Mag- 
netic Field — Principle of the Dynamo. 

this angle of inclination, 45°, and have, therefore, been emp- 
tied out. At the position of coil C, all the lines of force 
above it have been emptied out of the coil. The rate of 
change at this position is a maximum, and the induced E. 
M. F. then varies from in position A, to its maximum 
value at position C, 90° from A. If the motion be continued 
from C to D, many lines of force will now be emptied into 
it and induction will occur. The direction of the induced 
current is indicated, and is found by Fleming's rule. The 
induced E. M. F. gradually decreases during the motion from 
C to D, because the rate of change in the number of the lines 
of force increases in the same ratio as it decreased during mo- 
tion from B to C. Motion from D to E corresponds to that 
from A to B, and in E all the lines are again flowing through 
the loop, causing no induction at this position, since there is 
no rate of change. During the revolution of the coil through 



ELECTR OMA GNETIC IND UCTIOK 



305 



180°, from position A to E, the E. M. F. gradually increases 
from to a maximum of 90°, and gradually decreases again 
to at 180°. The same will be true of the second half of 
the revolution, 180° to 360°, except that the direction of cur- 
rent is the reverse, since moving a conductor up past lines of 
force produces an opposite direction of current from that 
obtained when it is moved down past the same lines. In one 
revolution of the coil there are thus two alternations of cur- 
rent, and two points of maximum E. M. F., at 90° and 
270°, and two points of zero E. M. F. — that is, when the 
current changes its direction at 0° and 180°. When this loop 
is mounted on a shaft and so rotated, Ave have the principle of 
a simple alternating current dynamo, or alternator, ^| 320. 

Faraday's Law is as follows : Let any Conducting Cir- 
cuit be Placed in a Magnetic Field ; then if by a 
Change in Position or a Change in the Strength of 





Fig. 275.— The Induced E. M. F. Depends Upon the Rate of Change of the 
Magnetic Lines Through the Loop — Faraday's Law. 

Field, the Number of Lines of Magnetic Force Pass- 
ing Through or Interlinked with the Circuit is 
Altered, an E. M. F. will be Induced in the Circuit 
Proportional to the Rate at which the Number of 
Lines is Altered. By referring to Fig. 275, it will be un- 
derstood how Faraday's Law applies to all our previous in- 
duction experiments. In the positions of the secondary cir- 
cuits shown by the solid lines, the number of lines through 
them is a minimum. When moved up close to the primary, 
as in the dotted positions, a great many more lines fill the 
coils, which are also emptied out again during recession. 

Lenz's Law, ^j 282, may also be applied to the motion of 
the coil in Fig. 274. The direction of current indicated by 
the arrows on the rings is found by Fleming's rule, and is 
20 



306 PRACTICAL ELECTRICITY. 

such that if the ring be viewed from the N-pole side as it is 
being moved away from this pole the induced current flows 
around it clockwise, producing a S-pole on this face with re- 
sulting attraction for the N-pole, from which it is receding. 
Muscular or mechanical energy must, therefore, be expended 
in moving the ring through the angular position in propor- 
tion to the electrical energy developed in it. 

292. Eddy Currents— Arago's Rotations.— When a 
magnet is suspended over a copper disc and the disc rotated, 
induced currents are generated in the disc, which tend to op- 
pose the motion producing them. If the magnet be free to 
move it will be dragged around in the same direction that the 
disc rotates. According to Lenz' s Law, the direction of the 
current in the part of the disc moving toward the magnet 
^ pole will be of the same polarity as the 

^0^~ \^§\ pole being approached, therefore tending 
/r'*V syt%y'~^\ ^0 repel the magnet, while that in the re- 
ti .'jy^r^ }j ceding part of the disc will be of the 
\j^r --1^ opposite polarity, thus attracting the 

^""■"""^pmnmafflf 5 ^ magnet. Both actions, then, tend to urge 
_ Fr M r magnet in the same direction and to 

rents induced in a Cop- cause its rotation. If the magnet be held 
per Disc Eotated Un- stationary and the disc revolved, consid- 

mantnt Mag^f ^ erabl y more force must be applied to 
turn it than when the magnet is not 
near it. Each part of the disc, as it comes under the influence 
of the magnet, is subjected to rapidly succeeding increases 
and decreases in the number of lines of force threading it. 

Such currents induced in masses of metals either by be- 
ing rapidly cut by the moving field or by moving in the 
field are called eddy currents. The direction of the eddy cur- 
rents in the copper disc for a particular case is shown in 
Fig. 276. The magnet is stationary and the disc rotated 
clockwise. The currents circulate around the disc in the 
form of two semi-circles. In the left-hand one the direction 
is anti-clockwise, producing a , N-face on the disc which re- 
pels the N-pole of the magnet, and tends to stop the motion 
producing it. On the right-hand side a S-face is produced, 
attracting the N-pole, and again tending to stop the motion 
of the disc, according to Lenz's Law. When the magnet is_ 
free to move, it will tend to move so that its poles will always 
be over the unlike poles induced in the disc, but as soon as 




ELECTROMAGNETIC INDUCTION. 307 

the magnet moves the paths of the eddy currents also change. 
They will always be set up with the magnet as their diame- 
ter, and each half of the disc will be of opposite polarity. 
The position which the magnet seeks is never attained and 
continuous rotation results as long as the disc is rotated. If 
pieces of wire gauze are pressed against the disc directly un- 
der each pole of the stationary magnet, Fig. 276, forming 
wiping contacts, or brushes, and the brushes connected to a 
galvanometer, the needle will be deflected by the eddy cur- 
rents when the disc is rotated. 

Faraday's disc dynamo consisted of a copper disc rotated 
between the two poles of a magnet, Fig. 277, the current be- 
ing led off from the centre and edge 
of the disc by brushes. Barlow's ^.^^^° UUo1 ^ 
wheel, Fig. 244, when rotated by 
hand will give current to an external 
circuit, illustrating the convertibility 
of a motor and dynamo. When 
electromagnets are used they must 
be excited by a separate source of 

Current. Fi £. 277.— The Eddy Currents 

A -m j. i Tend to Oppose the Motion 

A compass needle m a metal case Producing Them. 

will come to rest very quickly, 

because by its oscillating motion it induces eddy currents 
in the case which tend to stop the motion of the needle. 
The eddy currents circulating in solid conductors are converted 
directly into heat and are the source of much loss of energy and 
other derangements in dynamos, motors and transformers. 
To avoid them as far as possible, the solid conductor, as the 
iron core of an armature or induction coil, is made up of 
laminations, the plane of which is parallel to the lines of 
force of the field, See *j\ 332. Eddy currents circulate in the 
metallic bobbin of the D'Arsonval galvanometer coil when it 
moves in its magnetic field and tend to stop the mo- 
tion according to Lenz's Law. It is for this reason that the 
Weston instruments are so dead-beat. The same action also 
takes place in the copper disc rotated between permanent 
magnets in the Thomson wattmeter. 

Exp. 80 : Strongly magnetise a bar electromagnet and strike one 
pole with a piece of flat sheet copper and you find a cushioning effect 
is produced. You are unable to strike the pole with as great force as 
when the current is off. Eddy currents are induced in the copper, 



308 PRACTICAL ELECTRICITY. 

the reaction of the magnetic field of which tends to oppose the motion. 
The same is true if you try to quickly lift the sheet of copper from the 
pole. 

Exp. 81 : Suspend a copper penny by a thread between the poles of 
a horseshoe electromagnet. Twist the thread up and permit it to 
unwind. Send a current through the magnet and the motion of the 
penny ceases, due to the reaction of the eddy currents whichstop it, but 
when the circuit is broken the thread carrying the penny continues to 
untwist. 

Exp. 82 : Excite an electromagnet from a source of alternating cur- 
rent. Hold a piece of sheet copper over one pole, and it is strongly 
repelled, and if held there against the repelling force it will get very 
warm. The moving alternating current field cuts the copper sheet 
and eddy currents are induced as before. If the electromagnet has a 
solid iron core it will also get quite hot for the same reason. The cores 
of alternating current electromagnets are made of bundles of wire to 
increase their resistance to the flow of eddy currents. The rapid 
magnetisation and demagnetisation of the iron core of an electromag- 
net by an alternating current also produces heat as a result of the 
molecular friction between the particles of the iron, fl 30. A cer- 
tain amount of the electrical energy is converted into heat in this 
manner and is termed the hysteresis (hister-ee / -sis) loss. 

Hysteresis may be defined as the molecular friction between par- 
ticles of iron or steel when they are subjected to rapid changes in 
magnetisation. See If 336. 

293. Mutual Induction. — The induction due to two in- 
dependent electric circuits reacting upon each other is called 
mutual induction. The previous examples of induction in a 
secondary circuit due to current flowing in the primary cir- 
cuit illustrate mutual induction. Parallel conductors carry- 
ing independent alternating currents react upon each other 
by reason of the mutual inductive influence between them. 
Mutual induction in telephone circuits often gives rise to 
cross-talk unless the line is so constructed that the induction 
effects are neutralized, ^f 299. 

294. Self-induction. — Self-induction is defined as the cut- 
ting of a wire by the lines of force of the current flowing 
through it. When a current begins to flow along a wire the 
magnetic whirls spring outward from the wire and cut it. 
This cutting of the wire by its own lines of force induces in 
it a momentary inverse E. M. F., or an E. M. F. which op- 
poses the E. M. F. causing the current to flow, and is called 
a counter E. M. F. With a steady current the induction is 
only momentary, therefore a brief interval of time must elapse 
before the current passed through the circuit reaches its 
normal value. When the current flowing through the wire 



ELECTR OMA GNETIC IND UCTION. 309 

is stopped, the magnetic field collapses, and in so doing again 
cuts the wire, but in the opposite direction. A momentary in- 
duced E. M. F. is set up which is now direct, or in the same 
direction as the E. M. F. which previously caused the cur- 
rent to flow. The effects of self-induction are therefore to 
oppose the starting of a current by reason of the inverse E. 
M. F. which must be overcome before the current can flow, 
and to momentarily retard the cessation of the current by 
reason of the direct induced E. M. F. when the circuit is 
broken. Momentary currents of self-induction are also pro- 
duced in any circuit by any change in current strength 
through it, whereby the number of lines of force surrounding 
or interlinked with it is increased or decreased. 

The effects of self-induction are scarcely noticeable in a 
straight wire carrying a current, but when it is coiled up, as 
in a helix the magnetic field of every turn cuts many adja- 
cent turns and the E. M. F. is increased, being proportional 
to the current, the number of turns and the magnetic lines through 
the coil. When the coil contains an iron core the effects of 
self-induction are very much greater. One very noticeable effect 
is the bright spark appearing at the point of breaking a circuit 
containing wire wound around an iron core. No effect is 
noticed on closing such a circuit on account of the counter 
E. M. F., but at break a spark appears, due to the momentary 
induced direct current which tends to prolong the current in 
the circuit. The induced E. M. F. at break is very much 
higher than was the applied E. M. F. This induced current 
of self-induction is sometimes called the extra current. If the 
terminals at the point of break are held, one in each hand, 
and then separated, the body will receive a shock, the in- 
tensity of which will depend upon the size of the coil and the 
current used. No shock will be felt upon placing the hands 
across the battery, thereby indicating that the E. M. F. of 
self-induction is much higher than the battery E. M. F. 

295. Gas Lighting Spark Coil. — The function of the 
spark coil used in electric gas lighting is to increase the self- 
induction of the circuit at break, as when the chain of a 
ratchet burner is pulled. A coil is inserted in series with the 
battery circuit and the burner, and the heat of the spark on 
breaking the circuit is sufficient to ignite the gas. 

Such a coil, Fig. 278, consists of about 2 pounds of No. 16 insulated 
copper wire wound around an iron core 1 inch in diameter and 8 



310 



PRACTICAL ELECTRICITY. 




Fig. 278.— Gas Igniting Spark 
Coil with Laminated Core. 



inches long. The core is not solid, but consists of a bundle of soft 
iron wires, which greatly increases the inductive action by dimin- 
ishing the eddy currents, \ 292. 

Exp. 83 : Connect a galvanometer in parallel with a helix of fine 
wire, Fig. 279. Close the circuit and the needle is deflected, say to 
the right of zero, and the current divides between the galvanometer 
and the helix. Move the needle, by hand, to the zero position, and 

place some obstacle in the way so as to 
prevent it turning again to the right of 
zero. Now release the battery key and 
a momentary current, due to the self- 
induction of the helix, flows around 
the galvanometer needle, momentarily 
deflecting it in the opposite direction. 
The induced current through the helix, 
at break of circuit, is in the same 
direction as the battery current was, but flows in the opposite direc- 
tion through the galvanometer connected to it. This is shown by the 
dotted arrow in the figure. 

Exp. 84: In Fig. 279 an incandescent lamp is connected in shunt with 
an electromagnet and through the switch, K, to a battery of an E. M. F. 
equal to that required by the lamp. The resistance of the magnet 
should be such that with current flowing the lamp filament is just 
perceptibly red. At the instant of closing the switch the momentary 
self-induction of the 
electromagnet acts like 
resistance against the 
current, causing most 
of it to flow through 
the lamp, which glows 
brighter for a moment 
and then becomes dim 
as the current attains 
its steady value. On 
breaking the circuit 
the lamp again glows 
very brilliantly since 
it is in circuit with the 
electromagnet. The energy stored in the magnetic field is thus con- 
verted into a momentary direct current of a high E. M. F. and lights 
the lamp. The fields of a dynamo should not be broken when fully 
excited since the E. M. F. may become so high as to cause a puncture 
of the insulation at two or more points, and thus complete the circuit 
through the iron core, and cause a ground, ^ 312. The self-induction 
at break of such a circuit is termed the field discharge. 

296. Inductance. — The cause of the self-induction is due 
to the property possessed by the wire or coil called inductance, 
just as the resistance of a wire is that property of it which 
opposes the flow of a current through it. A coil or wire, 
therefore, possesses inductance whether current is passing 



\ Switch 



Battery, 
•Hell*: 



wmm 




l — illinium— ' 



Fig. 279. 



-Experiments Illustrating the Extra 
Current of Self-induction. 



ELECTR OMA GNETIC IND UCTIOK 311 

through it or not. The amount of inductance offered by a 
coil depends on the number of turns of wire in the coil and 
on the magnetic conductivity of the medium surrounding it. 
A coil of 50 turns wound around an iron core has a very 
much higher inductance than a coil of 50 turns without an 
iron core. A coil of 15 turns wound on an iron core has less 
inductance than one of 60 turns wound on a similar core. 
The inductance of a coil or circuit is measured by the E. M. 
F. induced in it when the inducing current varies at any 
given rate. The unit of inductance is called the henry (the 
symbol for which is "L"), and is the induction produced 
in any circuit when the induced E. M. F. is one volt, and 
the current through the circuit varies at the rate of one am- 
pere per second. The secondary coil of a 2-inch spark coil, 
^j 306, has an inductance of about 51 henrys ; a 2.5 ohm 
electric bell, .012 henry or 12 millihenrys ; the fields of a 
3.5 K. W. 100- volt, shunt dynamo, 13 henrys. 

297. Reactance and Impedance. — When an alternating 
current flows through a circuit containing inductance, the 
effects of self-induction will become continuous instead of 
momentary, and will considerably retard the flow of current 
through the circuit as long as it is maintained. The appar- 
ent resistance of a circuit to an alternating current is greater 
than the ohmic resistance. The cause of this apparent addi- 
tional resistance is due to the effect of self-induction, and is 
termed inductive resistance, or reactance. Reactance is the 
effect of self-induction expressed in ohms. It, therefore, dif- 
fers from inductance in that it exists only while the current 
flows. A coil has no reactance unless the current flows 
through it and the rate of flow is varied. This spurious re- 
sistance (reactance) in any circuit is measured in ohms, and 
is equal to the product of its inductance, the number of times 
the current flow is reversed per second and a constant 
(6.28). Ohm's Law, in its simplest form, is thus not 
applicable to calculations of circuits for alternating currents. 
The R in Ohm's Law for alternating currents includes the 
calculation of the resistance of the circuit plus the calcula- 
tion of its reactance. The total opposition offered to the 
flow of an alternating current by the resistance and the re- 
actance is called the impedance. On account of the reactance, 
a larger size of conductor must be used in alternating current 
circuits than when direct currents are used. 



312 



PRACTICAL ELECTRICITY. 




Fig. 280.— Effects of Self- 
induction. 



298. Choke Coils.— 

Exp. 85 : In Fig. 280 a solenoid of several ohms resistance wound 
in the ordinary manner, is connected in series with an incandescent 
lamp and to a source of direct current (D. C. ) by throwing the switch, 
S, down. The brilliancy of the lamp is practically the same with the 
solenoid in circuit as when it is cut out by the key, K. Neither is 
there any change in the lamp when an iron core is inserted in the 
coil. Now the circuit is connected to a 
source of alternating current (A. C. ) by 
throwing S up. With the solenoid out of 
circuit the lamp burns as brilliantly as be- 
fore, but when it is inserted, as by opening 
key, K, the lamp burns dimly. The cur- 
rent through it has been decreased by the 
self-induction of the solenoid. If an iron 
core is now gradually inserted in the coil, 
the current is gradually decreased, since the 
inductance is being increased, and the lamp 
may not give any illumination. The self- 
induction chokes back the current, so that less current is taken from 
the line. A device for regulating the candle power of lamps in an 
alternating current circuit is based on this principle, and is called a 
choke coil. The flow of alternating currents can thus be regulated 
much more economically than direct currents, since in the latter case 
regulation is effected by absorbing the energy in the extra resistance. 

Exp. 86 : The following measurements 
made on a coil of wire wound inductively 
when carrying a direct and alternating 
current will further illustrate the prop- 
erty of self-induction. In Fig. 281 the 
coil AB, without an iron core, is con- 
nected in series with an electrodyna- 
mometer and to a source of direct cur- 
rent. The pressure required to cause a 
known current to flow through the coil 

is 30 volts. The coil is then subjected to an alternating current 
pressure of such a value that the amperes through it, as indicated by 
the dynamometer are the same as before, and the potential difference 
across it is found to be 100 volts. A pressure of 100 volts alternating 
current is therefore required to send the same current through the 
coil as was maintained by 30 volts direct current. The difference in 
the two pressures is required to overcome the opposition due to the 
self-induction. 

299. Neutralizing the Effects of Self-induction— In- 
ductive and Non-Inductive Circuits. — Self-induction in a 
coil may be neutralized by winding one-half of the coil in a 
right-hand direction and the remainder in the opposite direc- 
tion. This is accomplished in practice by folding the length 
of wire to be used at its middle point and starting at this 
point, winding both halves as a single wire, when the termi- 




Fig. 281.— Effects of Self- 
induction. 



ELECTROMAGNETIC INDUCTION. 313 

nals will be conveniently arranged for connection. The mag- 
netic effects of the current flowing in one direction neutralize 
those of the same current flowing in the opposite direction 
and the coil now offers practically the same resistance to 
either an alternating or direct current. Such a circuit is said 
to be non-inductive and contains practically no inductance, 
while an ordinarily wound coil constitutes an inductive cir- 
cuit No polarity would result from inserting an iron core 
in a non-inductively wound coil since the current through 
one-half of the turns would tend to magnetise one end with a 
N-pole,while in the other half the tendency would be to pro- 
duce a S-pole at the same end. 

The coils of laboratory rheostats and Wheatstone bridges 
are wound non-inductively, Fig. 126, so that they will have 
no magnetic influence on a galvanometer, and also so that the 
currents in the bridge arms may reach their maximum value 
simultaneously. Self-induction is neutralized in alternating 
current lighting and power circuits by placing the lead and 
return wires as close together as possible. For this reason 
concentric cables are used for such circuits. An incandescent 
lamp is practically a non-inductive resistance, while an electro- 
magnet is an inductive resistance. 

QUESTIONS. 

1. The N-pole of a bar magnet is thrust through a key ring and 
quickly withdrawn without touching it ; the action is continued for 
a time and the ring becomes warm. How do you explain this ? 

2. Is the direction of the induced current in question 1 clockwise 
or anti-clockwise, as viewed from the side next to you, when the bar 
magnet is withdrawn from the ring? Make a sketch. 

3. State three factors upon which the induced E. M. F. is depend- 
ent when conductors are moved through a magnetic field. 

4. A cell connected to a galvanometer indicates 50 deflections. A 
portion of the connecting wire is coiled up and an electromagnet ex- 
cited from another cell is plunged into the coil. The galvanometer 
needle momentarily indicates only 30°. Explain this and make 
sketch to illustrate your answer. 

5. The two ends' of a 5-pound reel of bell wire are connected to 
each other, and it requires more muscular force to quickly insert and 
remove an electromagnet from the centre of the reel than when the 
tw T o ends are free. Explain fully. Make sketch. 

6. The E. M. F. of a dynamo is toolow T and the field cores are fully 
saturated so that the voltage cannot be raised in this manner. How 
would you increase it and still use the same machine ? 

7. Two sets of parallel independent circuits supply current to some 
incandescent lamps. At the instant of turning out ail the lamps on 



314 PRACTICAL ELECTRICITY. 

one set of mains the others burn more brightly. Explain fully and 
give detail sketch of the direction of currents in the circuits, etc. 

8. An electromagnet is inserted in a coil of wire and the terminals 
of the latter then joined to a galvanometer but there is no momentary 
deflection of the needle. Explain why. 

9. At the instant of breaking the electromagnet circuit in ques- 
tion 8 the needle is deflected 40°, while on making it again the deflec- 
tions are only 35. Explain this and make sketch. 

10. Two pieces of thick copper wire are joined to a battery, and when 
the ends are brought in contact and separated there is no perceptible 
spark. An electromagnet of high resistance is connected to the same 
battery and a bright spark appears when the circuit is broken. Since 
the E. M. F. of the battery is the same as before and the resistance so 
much higher than before, how do you account for the phenomenon ? 

11. A solid iron core electromagnet is excited by an alternating cur- 
rent. The core becomes very hot though the wire is sufficiently large 
to carry the current without becoming warm. State two reasons for 
the heating. 

12. Using a copper mallet, why is it impossible to strike the pole of 
a strong electromagnet with as hard a blow as when the magnet is 
not excited ? 

13. State two phenomena occurring in the copper mallet when the 
pole of the electromagnet, in question 12, is struck. 

14. Make a sketch of a copper disc rotating between two horseshoe 
permanent magnets, as in the Thomson recording wattmeter. Indi- 
cate polarities and directions of rotation and eddy currents. 

15. Ten volts alternating current cause 5 amperes to flow through 
a straight insulated copper wire 20 feet long. The same wire is now 
coiled up and the current is only 3 amperes, yet the pressure and re- 
sistance of the wire are exactly the same .as before. How do you ex- 
plain this? 

16. Why is a choke coil more economical than a rheostat? 

17. The resistance of an electromagnet is 10 ohms but its apparent 
resistance to an alternating current is 15 ohms. What is meant by 
this expression? 



LESSON XXV. 



THE INDUCTION COIL. 



Principle of the Induction Coil or Transformer— The Induction Coil — 
Action of the Coil — Action of the Condenser — Construction of 
Induction Coils — Wehnelt Electrolytic Interrupter— Table XIX. 
Sparking Distances in Air — Spark Coil Data — Table XX. Spark 
Coil Dimensions— Vacuum Tubes— Roentgen Rays (X-Rays) — 
The Fluorescing Screen and Fluoroscope— The Telephone — The 
Microphone Principle — The Blake Microphone Transmitter — The 
Telegraph — The Signal System and Circuits — Electric Waves — 
Wireless Telegraphy — Questions. 

300. Principle of the Induction Coil or Transformer. — 

An induction coil, or transformer, consists of two independent 
coils in which, by induction, an alternating or interrupted 
electromotive force, maintained across one of the coils, is 
made to produce a higher or lower electromotive force in the 
other coil. Such a coil consists of three principal parts : 
the primary, the secondary, and the iron core. In Fig. 282 
two independent coils are wound upon an iron ring. When 
the secondary is connected to a 
galvanometer and a current passed 
through the primary from a bat- 
tery, the galvanometer needle 
will be momentarily deflected at 
"make" and "break" of primary, 
as in our previous experiments. 
The currents in the primary mag- 
netise the iron core, and the lines 
of force in the core thread through 
the secondary coil producing induction effects. If the battery 
current is sent through the secondary, induction is produced 
in the primary as before. This simple ring form of closed 
iron circuit transformer represents the principle of construc- 
tion in all induction coils or transformers. In Fig. 283 the 
iron circuit is of the open type and the primary wound 
upon an iron core, while the secondary is insulated from 
and wound on top of it. The induction is produced either 

315 




Fig. 282.— Closed Circuit 
Transformer. 



316 



PRACTICAL ELECTRICITY. 




Fig. 283.— Open 
Circuit Trans- 
former. 



by an interrupter in a direct current circuit or by an alternat- 
ing current. 

In all transformers the relation of the induced E. M. F. 
generated in the secondary circuit to that employed in the 
primary, is nearly proportional to the ratio of the number of 
turns in each circuit. For example, if the 
primary contains 100 turns and the secondary 
2000 turns, then the induced E. M. F. will 
be about twenty times as great as that used 
in the primary. If this secondary contained 
only fifty turns then the E. M. F. would be 
only half as great as that in the primary. 
By a proper proportioning of the turns, then, any desired 
E. M. F. may be obtained from the secondary terminals. 

The function of an induction coil is to transform the energy 
delivered to its primary from any given voltage to a higher 
or lower voltage. While a current of low pressure may thus 
be transformed into one of a very high pressure, the latter 
loses in current what it gains in pressure, so that the watts 

in the secondary 
are no greater 
than those de- 
veloped in the 
primary, but al- 
ways a little less, 
owing to various 
losses in trans- 
formation and 
the C square R 
loss in the sec- 
ondary circuit. 

301. The In- 
duction Coil. — 
The principle of 
the transformer is utilized in induction coils constructed to 
generate very high electromotive forces, capable of overcoming 
the resistance of the air and causing sparks to pass across air 
gaps. The induction coil, or Rhumkorff's inductorium, Fig. 
284, is a step-up-transformer since, by induction, it raises the 
voltage of several cells connected to its primary to thousands 
of volts at the secondary terminals. It consists of a straight 
laminated core, made up of a bundle of soft charcoal iron wires 




IS 



Fig. 284. — Induction or Spark Coil. 
For use with direct currents. 



THE INDUCTION COIL. 



317 



around which is wound the cylindrical primary coil, com- 
posed of several layers of heavy wire, while a secondary coil 
composed of thousands of turns of fine wire, is wound over 
the primary, similar to Fig. 283. The inner or primary coil 
is connected to a battery through an automatic interrupter, 
Fig. 285. At the " make " and the " break " of the primary 
circuit currents are 
induced in the sec- 
ondary according to 
the laws of induc- 
tion, % 284, and 
appear as a series 
of sparks passing 
through the air from 
one secondary ter- 
minal to the other. 
The general appear- 
ance of such a coil 
is shown in Fig. 
284, and its connec- 
tions, in Fig. 285, 

Exp. 87 : The student's induction coil illustrated in Fig. 266, may 
be mounted on a base provided with a contact screw and vibrator 
arm, when induced currents can be produced automatically from the 
secondary coil. This arrangement is shown in Fig. 286, where the 
connections can be readily traced. Using the primary alone, the 
automatic action of the electric bell is illustrated. When short lengths 

of brass tubing are attached to 
|I_battery t ^ e secondary terminals and 
then clasped, one in each hand, 
a peculiar muscular contraction 
is produced, due to the high 
voltage of the induced E. M. F. 
This is the physiological effect 
of an electric current, f 96. 

302. Action of the Coil. 

The action of the automatic 
interrupter used on induc- 
tion coils is shown in Fig. 




Condenser 



Fig. 285. — Diagram of Connections of a Spark Coil. 




Fig. 286. — Student's Induction Coil as a 
Spark Coil. 



285. The current from the battery flows through the soft iron 
pivoted armature, A, free to move, to the stationary contact 
post, C, the armature being held in contact with the point, C, 
by the spring, S. From C the current circulates around the 
primary core and returns to the battery. The contact screw ter- 



318 



PRACTICAL ELECTRICITY. 



minates in a piece of platinum wire and there is also a piece 
of sheet platinum fastened to the vibrator arm at the point of 
contact with the screw C. Platinum is used to prevent the 
oxidation due to the spark at the contact points. The instant 
the current flows through the primary coil it strongly mag- 
netises the iron core, NS, which core attracts the armature by 
overcoming the tension of the spring. This breaks the primary 
circuit, the magnetism of the core ceases, and the spring pulls 

back the armature again " mak- 
TiNroa ing " the circuit so that the same 



events are repeated. The armature 
vibrates continually as in an elec- 
tric bell, and the circuit is "made" 
and " broken " thousands of times 
per minute. An inverse induced 
current in the secondary corre- 
sponds with each " make " of pri- 
" direct " current is induced on " break " of pri- 

pro- 











/ 






/ 






- 




wmw 


^^mm 




£T 






/ 



PAP E Ft, 



Fig. 287.— Detail of Condenser 
Construction. 



mary, while a 

mary. Interrupted currents in the primary, therefore 

duce alternating currents in the secondary. 

The self-induction in the primary circuit has a very import- 
ant bearing upon the action of the coil. At " make " of pri- 
mary the counter E. M. F. opposes the battery current, and 
reduces the time rate of change of the current upon which the 
induced E. M. F. depends, while at " break," the self-induced 
current in the primary tends to pro- 
long or increase the primary current, 
preventing its rapid fall to zero by 
sparking across the break. A rapid 
rate of magnetisation and demagnet- 
isation of the iron core means a great 
rate of change of the lines of force 
threading through the secondary coil, 
and hence a high E. M. F. A con- 
denser, H 303, is added for the purpose of suppressing this 
spark across the primary break and of aiding the primary 
current to fall abruptly to zero. 

303. Action of the Condenser. — A condenser for a spark 
coil consists of two sets of interlaid layers of tin-foil separated 
by sheets of paper coated with paraffin or shellac, Fig. 287. 

The alternate layers of tin-foil are connected to each other, 
and two common terminals are thus formed, as depicted in 




Fig. 288.— Plates of a Con- 
denser Asseiubled and 
Connected. 



THE INDUCTION COIL. 319 

Fig. 288. There is no electrical connection between the con- 
denser terminals, but if they are connected to a source of 
very high E. M. F. the plates become electrified or charged, 
and may be discharged when a proper path is afforded. The 
condenser is located in the base of the coil shown in Fig. 284, 
and its terminals connected across the primary break, points 
A and C of Fig. 285. 

The condenser action is as follows: when current flows 
through the primary at " make, " Fig. 285, no energy 
can be stored up in the condenser, but it appears as the 
magnetic field in the core and surrounding primary. At 
" break " the extra current of self-induction in the primary, 
instead of overcoming the resistance of the spark-gap, 
charges the condenser, and the core is more quickly demagnet- 
ised. At " break " also there is a complete discharge circuit for 
the condenser back through the battery and the primary coil, 
in the opposite direction to the previous primary current ; the 
condenser thus aids in 
quickly demagnetising the ° A 

iron core by tending to set Q I \\\\\\\\\\\\\ I 

up lines of force in the 
opposite direction, 
primary current is re-made 
before the reverse condenser 
current disappears, as is rig> m _ Primary Shock Coil . 
practically the case, the bat- 
tery current has to first overcome this obstructing current 
before it can produce any effect. Thus the inductive 
effect of the " make " circuit is retarded by the condenser. 
With the use of a condenser then the E. M. F. of the 
" direct " secondary current at break is exalted, while that 
of the " inverse " secondary current on " make " is dimin- 
ished. The consequence is that when the secondary dis- 
charge has to overcome much resistance only the former 
current is able to pass, and the secondary discharge becomes 
practically an intermittent current of high voltage in one direction 
only. In medical induction coils where no condenser is used 
the secondary charges are practically equal. 

The voltage generally applied to the primary of the ordinary 
induction coil varies from about 4 to 15 volts according to the 
size. A higher voltage causes excessive sparking and destruc- 
tion of the platinum contacts. Specially constructed inde- 



in tne jru 
If the ,_T 
3-made 



320 PRACTICAL ELECTRICITY. 

pendent vibrators are used with modern high class coils which 
can be connected directly to an electric light circuit of 110 
volts or more. The vibrator is practically a relay, ^[ 313, 
which makes and breaks the current in the independent pri- 
mary circuit by means of another pair of platinum contact 
points. This circuit can also be supplied from a 110-volt cir- 
cuit and the current regulated by a rheostat. 

304. Construction of Induction Coils.— Induction coils 
may be divided, according to their use, into two general 
classes, medical or therapeutic coils and spark coils. In the 
former, the winding is designed so as not to produce such a 
high E. M. F. as in a spark coil, and consequently no con- 
denser is required. Some means for varying the intensity of 
the shock is provided, such as altering the number of turns 
in circuit in the secondary coil by a selector switch, or by so 
constructing the secondary that it may be gradually with- 
drawn from the primary. Regulation may also be effected 
by varying the position of a brass tube enclosing the iron 
core. 

The tube screens the iron core from the action of the pri- 
mary current, thereby weakening the magnetic field cutting 
the secondary circuit. Instead of magnetising the core, a 
portion of the energy of the primary circuit is thus expended 
in producing eddy currents in the tube. The iron core is com- 
posed of a bundle of soft charcoal iron wires, about No. 22 
gauge. For medical coils the number of layers in the pri- 
mary is generally from 4 to 6 and the size of wire used No. 
24, 22, or 20, according to the dimensions of the coil, while 

the secondary is wound with No. 
34 or 36. The primary will thus 
have considerable self-induction 
which is not a great disadvantage 
in these coils. 

Spark coils are usually rated 
according to the number of inches 
Fig. 290.— Sectional Winding of that the spark will lump between 

theSecondaryofaSparkCdl. ^ ^Jj^y terminals through 

the air. Thus a two inch coil means that the E. M. F. is 
high enough to cause sparks to pass when the terminals 
are separated at a distance of two inches. The self-induction 
of the primary must be very low and so it is wound with 
about 2 layers of a much larger size wire than that used 




THE INDUCTION COIL. 



321 



in medical coils. The primary must be thoroughly insulated 
from the secondary, and also the coils of the secondary from 
each other when it is wound in sections. With insufficient 
insulation the induced E. M. F. is liable to cause a spark to 
pass from the secondary to the primary, or between sections 
of the secondary, instead of across the terminals. When the 
insulation is so punctured by the spark at two or more points 
the spark will always thereafter take the path of least resist- 
ance, in preference to that between the secondary terminals. 
When the coil is designed to produce a spark over 1.5 inches 
the secondary should be wound in a number of sections sep- 
arated from each other by proper insulation. In Fig. 290, 
the secondary is wound in two sections as the potential differ- 
ence between layers is less than when wound in a single coil. 
The sections must be so connected that the current will circu- 
late through all of them in the same direction. 

In Fig. 284 a commutating switch for reversing the cur- 
rent in the primary circuit, is mounted near the left-hand 
end of the base, thereby changing the polarity at the sec- 
ondary terminals. Another selector switch near the centre of 
the base serves to connect more or less of the condenser's ca- 
pacity across the points of "break." The following table 
gives the sparking distance and approximate corresponding 
E. M. F. between opposed sharp needle points : 

Table XIX.— Sparking Distances in Air. 



Volts. 


Distance. 
(Inches.) 


Volts. 


Distance. 
(Inches.) 


5000 


.225 


60000 


4.65 


10000 


.47 


70000 


5.85 


20000 


1.00 


80000 


7.1 


30000 


1.625 


100000 


9.6 


35000 


2.00 


130000 


12.95 


45000 


2.95 


150000 


15.00 



Note.— These values are correct for effective sinusoidal voltages. 

305. Wehnelt Electrolytic Interrupter.— Instead of the electro- 
magnetic vibrator previously described, the electrolytic effect of the 
current may be utilized to break the primary current of an induc- 
tion coil. The Wehnelt interrupter consists of a vessel containing 
dilute sulphuric acid in which is immersed a lead plate and a glass 
tube having a small piece of platinum wire (about \ inch of No. 24) 
21 



322 PRACTICAL ELECTRICITY. 

sealed in its lower end. External connection is made with the pla- 
tinum wire by filling the tube with mercury, or as in the electrode 
in Fig. 94. If this electrolytic cell be connected to a source of suffi- 
cient power so that 12 volts or more are maintained across. it, with 
the platinum as the anode* and the lead plate as the cathode, gases will 
be liberated by electrolysis. The oxygen gas enveloping the pla- 
tinum tip practically insulates it from the solution, and the circuit is 
interrupted when the evolution of gas ceases and the circuit is again 
" made." The action is very rapid, and the " makes " and " breaks " 
quick and sharp. The cell emits a buzzing noise and a yellowish 
light surrounds the platinum wire. A AVehnelt interrupter connected 
in series with the primary of a small spark coil will cause it to give a 
much larger spark than when the mechanical interrupter is used. 
The frequency of the interrupter depends upon the area of platinum 
exposed, the self-induction of the coil and the voltage. This inter- 
rupter in series with the primary coil may be operated from 110 volts. 
Prob. 116 : The primary of an induction coil is wound with 100 
turns of No. 14 copper wire and the secondary, with 35,000 turns. 
Ten volts cause a current to flow through the primary. What is the 
approximate E. M. F. at the secondary terminals ? 

By \ 300, -Taa - = 350, or there are 350 times as many turns on the 
secondary as on the primary. 

10 X 350 = 3500 volts, secondary. 
E = 10 volts in primary, ratio of transformation = 350. 

Prob. 117 : The resistance of the primary in Prob. 116 is 0.5 ohm, 
and if the loss in conversion of the energy to the higher potential is 
50 per cent what will be the approximate current strength in the 
secondary circuit ? 

F 10 
By Formula ( 28 ) C = ^ = -? = 20 amperes in primary. 

By Formula (62) W = E X = 10 X 20 = 200 watts in primary. 
50% of 200 watts = 100 watts in secondary. 

W 100 
By Formula (63) C = jr = g^ =.028 ampere. 

Note. — The above problem is only approximate, since other factors enter into the 
calculation. It should assist, however, in understanding the relation between the ex- 
pended primary energy and that appearing as a high potential spark in the secondary. 

306. Spark Coil Data. — The following dimensions are 
given for several sizes of spark coils, similar to that depicted 
in Fig. 284, so that the student may be guided if he attempts 
construction, f 

* If the platinum wire be connected by mistake as the cathode, it will be melted. 
See i 264. 

f In a book entitled Induction Coils and Coil Making, by Allsop, will be found com- 
plete data for constructing and operating spark coils. The data for a 12 inch coil, as 
given, requires 12 pounds of No. 36 silk covered wire, or about five miles in length. 



THE INDUCTION COIL. 
Table XX. — Spark Coil Dimensions. 



323 



Length of spark. 

Size of bobbin 
ends 

Length of bob- 
bin .... 

Length and di- 
ameter of core. 

Size of base . . 

Size of tinfoil 
sheets . . . 

Number of tin- 
foil sheets . . 

Size of papei 
sheets . . 

Primary coil . . 



Secondary coil 



| inch 


2iXH 


4 


4^X T % 
1\ X 3£ X lj 


4X2 


36 


5X3 
No. 18 


fib. No. 40 



1 
J inch 


2* X A 


5* 


6X| 

9X5X2 


5JX Si 


40 


6JX 4k 

No. 18 


1 lb. No. 40 



1 inch 



i X 6 X II 

X 4 

40 



2 inches 

4 X 2f X 1 

6| 

12 X U X 3J 

6X6 

60 



9X5 ! — 

2 layers No. 2 layers 14 B. 
16, silkj W. G. silk 
covered. covered. 
lilbs.No.38i2Jlbs.No.36 



Two large induction coils, capable of giving a 45-inch 
spark between their secondary terminals, and weighing 1500 
pounds each, were recently constructed by an American firm 
for the Japanese government. The primary interrupter was 
actuated by a small motor and the rate of interruptions was 
capable of being varied between wide limits. With 40 volts 
maintained across the primary circuit, a current of 30 am- 
peres produced a very heavy 42-inch spark. 

Exp. 88 : The mechanical effect of the spark from an induction coil 
may be observed by holding a piece of cardboard between the termi- 
nals when the spark is passing. The card will be perforated, leaving 
a bur on each side. Thin plates of any non-conductor can be punc- 
tured in like manner. 

Exp. 89 : To observe the heating effect, place a small quantity of gun- 
powder on a glass plate and arrange the terminals of the coil so that 
the spark will pass through it. On closing the battery circuit, the 
heat developed by the spark causes the powder to explode. 

Exp. 90 : The chemical effect is illustrated by moistening a piece of 
blotting paper with the solution used in the polarity indicator, % 106. 
Attach one of the secondary terminals to the edge of the paper, hold 
the other in the hand by an insulator, and trace designs on the paper 
when the coil is in action. The discharge decomposes the chemical 
salt, as shown bv the blue mark. The action is the same as given 
in i| 106. 

307. Vacuum Tubes. — Vacuum tubes, first devised by 
Geissler, are thin glass tubes, variously shaped and provided 



324 



PRACTICAL ELECTRICITY. 




Fig. 291.— Geissler Tube. 



with a platinum connection at each end of the tube, which 
extends a short distance into it. The tubes are then partially 
exhausted and filled with either a gas, liquid, or solid, and 
sealed up. On connecting the terminals to the secondary of 
a spark coil, and starting the coil 
in action, a beautiful discharge 
takes place, filling the tube with 
a luminous glow. The fluorescent 
effect depends upon the material 
introduced into the tube. The 
electric spark will not pass through a vacuum. The high 
potential maintained across the tube causes the molequles of 
gas to become positively and negatively electrified, and the 
resulting attractions and repulsions which occur produce a 

violent molec- 
ular bombard- 
ment, causing 
the fluorescent 
effect. 

308. Roent- 
gen Rays (X- 
Rays).— While 
experimenting 
with a vacuum 
tube, excited 
from an induc- 
tion coil, William 
Roentgen, of 
Germany, dis- 
covered that a 
sensitized photo- 
graphic plate, 
concealed from 
daylight, but 
lying near the 
vacuum tube, in- 




Fis?, 292. 



-Radiograph of the Human Foot in a Shoe. 
Made by Roentgen rays. 



dicated exposure to light when developed. Upon further 
investigation he found that a light was emitted from the 
vacuum tube, not perceptible to the human eye, but 
capable of penetrating many substances, as wood, metal, 
paper, etc. When different substances are interposed between 
a protected sensitized plate and an excited vacuum tube, 



THE INDUCTION COIL. 



325 



capable of producing rays of this light, it penetrates them 
with different intensities, according to their density, so that 
the sensitized plate, upon development, shows the shadows of 



the objects inter- 
made from such a 
When the human 
protected plate and 
affected directly un- 
they are nearly 




posed. A photographic print 
negative is termed a radiograph. 
hand is placed between the 
the tube the plate is scarcely 
derneath the bones, because 
opaque. Considerable light 



Fig. 293— Focus Tube for X-Ray Work. 

penetrates the flesh and affects portions of the plate directly 
underneath it. A print made from such a negative gives 
shadows of the bones and a faint outline of the flesh. The 
shadows of the bones in all animal bodies can thus be made, 
and broken bones and 
foreign objects, such 
as bullets, needles, etc., 
accurately located. 

A radiograph of the 
human foot in a shoe 
is illustrated in Fig. 
292. The nails of the 
shoe, etc., as well as 
the bones of the foot, 
are clearly discernible. 
Professor Roentgen 
first called the rays of 
this peculiar light X- 
Rays, but they are 
usually named in his 
honor, Roentgen rays. 
A common form of 
tube used in X-ray work, called a focus tube, is illustrated 
in Fig. 293. A concave aluminum reflector extends a short 
distance inside the glass tube and a wire attached thereto 
terminates at point B. This reflector is connected to the 




Fig. 294. 



-Examining the Bones of the Hand 
by the Fluoroscope. 



326 



PRACTICAL ELECTRICITY. 



negative pole of the induction coil and forms the cathode of 
the tube. The anode is a piece of sheet platinum inclined at 
about 40° to the axis of the tube, similarly connected to the 
positive pole of the induction coil at point A. The tube is 
exhausted to a fairly high vacuum and the X-rays emanate 
from the tube below the platinum anode. 

309. The Fluorescing Screen and Fluoroscope.— A 
piece of paper or board coated with certain crystals, as platino- 
barium cyanide, or tungstate of calcium, and placed near a 
fluorescing vacuum tube in a darkened room, becomes a 
fluorescent screen, whether it be looked at from the crystal coated 
or the opposite side. The light is of a pale greenish yellow 
cast. If the hand be interposed between such a screen and 
the tube, the shadow of the bones can be plainly seen on the 
screen, the bones intercepting some of the Roentgen rays, and 
thus causing the shadow. Wood readily allows the rays to 
pass through it, so that if an inch board be held between the 
hand and the screen, the shadow is still visible. In the 
fluoroscope such a fluorescing screen forms the bottom of a 
box, the opaque sides of which slant inward toward the top 
where an opening is left for observation, Fig. 294. The day- 
light is thus ex- 
cluded and the 
shadows of objects 
interposed between 
the fluoroscope and 
the tube are plainly 
visible upon the 
enclosed fluoresc- 
ing screen. Fig. 
294 illustrates the 
manner of viewing 
the bones of the 
hand. The tube is 
not generally en- 
closed, however, as 
shown in the cut. 

310. The Tele- 
phone. — An in- 
strument designed for the transmission of articulate speech 
by an electric current is called a telephone. A section and 
perspective view of a Bell telephone is shown in Fig. 295. A 




Fig. 295. — Transmission of Speech by the 

Bell Telephone. 
The transmitter and receiver are exactly alike. 



THE INDUCTION COIL. 



327 



small spool of fine wire encircles one end of a bar magnet 
mounted in a rubber tube, the ends of this coil being carried 
to the far end of the tube and connected to the binding posts, 
PP. A thin circular iron diaphragm is located very close to 
the pole of the magnet, at the coil end, and is supported by a 
conical-shaped piece of rubber, attached to the tube, which 
serves either as a mouthpiece or ear trumpet. When two 
such instruments are connected by wires, as in Fig. 295, 
either one may be used as a transmitter and the other as a 
receiver. No battery is required. 

When a person talks to the disc of the transmitter, A, the 
sound waves striking it cause it to vibrate. The disc is mag- 
netised by induction from the magnet's pole, and as it vibrates 
the number of lines of force threading through the coil are 
constantly being increased and decreased as the disc ap- 
proaches and recedes from the coil. Alternating induced cur- 
rents are thus set up in the coil, which currents flow through 
the line to the coil of the receiver at B. When the direction 
of the arriving current is such as to reinforce the magnetism 
of the receiver's magnet its disc is strongly attracted, and 
when the current produces a demagnetising effect the disc flies 
back. The disc of the receiving telephone is thus compelled 
to repeat every movement of the disc in the transmitter, and 
the vibrations of the receiver 
produce sound in the same 
manner as the vibrations of 
a drum. This telephone 
transmitter is practically an 
alternating current dynamo, 
driven by the energy of the 
human voice, while the re- 
ceiver is a motor driven by 
the current from the gen- 
erator. 

311. The Microphone 
Principle. — A microphone 
is a device for rendering 
faint or distant sounds dis- 
tinctly audible, and is used in many telephone transmitters, 
H 312. The principle involved is the production of an unsteady 
electric current by a variable resistance introduced into the 
circuit. A simple form is illustrated in Fig. 296. A and B 




Fig. 



296. — Apparatus to Illustrate 
the Principle of the 
Microphone. 



328 



PRACTICAL ELECTRICITY. 



are two carbon buttons one of which is fastened to a thin 
pine wood sounding board and the other to a brass spring, S, 
which causes B to touch A. The buttons are connected in 
circuit with a telephone and battery. While the current is 
flowing the least motion, caused by sound waves or other 
means, will vary the contact resistance between the buttons, 
and thus vary the current strength in the telephone circuit. 
The induced currents in the telephone cause the disc to 
reproduce the original sounds. The telephone may be located 
at a considerable distance from the microphone, when the 
reproduced sound, as the ticking of a watch, will be as 
audible as though produced close to the ear. 

312. The Blake Microphone Transmitter. — The in- 
duced electric currents set up by the human voice in the Bell 



Seconoary ,__ 





Fig. 297.— Connections of a Telephone System for Two Stations. 
Blake microphones are used as transmitters and Bell telephones as receivers. 



telephone, become materially weakened when they have to 
flow over lines of considerable length and resistance, so that 
the sounds in many cases become inaudible. In commercial 
telephone systems the Bell telephone is used as a receiver 
only, the microphone principle being used in the construc- 
tion of the transmitter, so that the sound of the voice is 
only required to regulate or vary an electric current already 
generated by a battery, instead of being used to generate the 
current. The general arrangement of two telephone stations 
will be understood from Fig. 297. Each transmitter is a 
microphone, in which the spring, S, supports a small carbon 
button, A, against which rests the hammer shaped end, B, 
of another spring, C. The springs are insulated from each 



THE INDUCTION COIL. 



329 




298.— Telegraph Trans- 
mitting Key. 



other, and are connected in series with a battery circuit and 
the primary of a small induction coil. 

Sound waves cause a vibration of the diaphragm, D, and 
the varying pressure it exerts between the carbon button and 
the hammer, causes variations in the battery circuit, as in the 
microphone. The induced secondary current flows through 
the receiver of station No. 1, and through the line to the 
Bell receiver and the secondary coil at station No. 2, causing 
the diaphragm of the receiver to 
vibrate in unison with that of the 
transmitter and so produce articulate 
speech. One wire from each receiver, 
as at points 2 and 3, may be con- 
nected directly to the earth through 
a gas or water pipe and a saving in 
copper effected by using only one transmission line. The 
system would then be working on a ground return, the earth 
acting as the other conductor. A ground is the contact of a 
conductor in any circuit with the earth, permitting an escape 
of current if another ground exists. 

313. The Telegraph. — The telegraph instrument is an 
apparatus for transmitting signals by the aid of an electric 
current. It consists of 
the line, the transmitter 
or key, the receiver or 
sounder, the relay and 
the battery. The line 
between two stations is 
generally a single iron 
wire with a ground re- 
turn. The transmitter 
key is depicted in Fig. 
298. It consists of a 

brass lever with its axis . Fi ^ 299. -Telegraph Sounder. 

pivoted at AA, carrying a platinum contact point, B, which 
is brought into contact by depressing the knob against the 
action of the spring, S. On depressing the lever by the knob, 
N, the two platinum points, B, P, connected to the line by 
posts C and D, are brought into contact and complete the 
circuit. When not in use the circuit is closed by the switch, 
K. The sounder, Fig. 299, consists of a brass lever with its 
axis pivoted at C, and carries an iron armature, A, of the 




330 



PRACTICAL ELECTRICITY, 



electromagnet, M, which is connected in circuit by two 
binding posts, P, P. A clicking sound is produced at each 
" make V of the circuit and a spring pulls the armature back 
on " break " of circuit. In long lines the current, due to the 
high resistance, may be so small as to render the clicks of the 
sounder inaudible, when a relay is used. A relay, Fig. 300, 
is a small switch operated by an electromagnet wound with 
many turns of tine wire. The magnet, M, is inserted in the 
main circuit by the posts, 3 and 4, and the platinum contact 
points, S, S, are brought in contact when the armature, L, of 
the magnet is attracted against the action of the spring, B. 
This switch, S, S, is inserted in a local circuit with a battery 
and sounder by the posts, 1 and 2, Thus a very weak cur- 
rent through the relay brings into action a strong local current 
which operates the sounder. 

314. The Signal System and Circuits. — A series of 
armature clicks separated by intervals of long or short dura- 
tion constitute the signals transmitted. A short interval 
between clicks is called a " dot," and a longer interval a 
"dash." By different combinations of the "dashes" and 
" dots " an alphabet is constructed and words spelled from 

the signals received. 
The alphabet devised 
by Morse is generally 
used. Low voltage 
dynamos or closed cir- 
cuit batteries are used 
for operating telegraph 
systems. 

Connections for 
three stations provided 
with relays and local 
m Fig. 3U1. When one of the stations 
to another the third also receives the signal, since 
relays are in series. The function of the small 
cut-out switch on the transmitter key is to preserve the con- 
tinuity of the line since it is in series with it, as shown in 
Fig. 301. 

315. Electric Waves. — The magnetic field surrounding a 
conductor through which a current is flowing changes for 
each change in current strength. When the current strength 
increases, the magnetic field around the conductor enlarges 




circuits 
signals 
all the 



-Telegraph Relay, 
are given in Fig. 301. 



THE INDUCTION COIL. 



331 



or expands outward in all directions, but with a decrease in 
current strength, the field returns again toward the conductor. 
If instead of a slowly increasing and decreasing current in 
any circuit we consider electric oscillations of very high 
rapidity, as the discharge of an induction coil, then part of 
the energy of the magnetic field is radiated off into space in 
all directions as electromagnetic waves corresponding to the 
ripples on the surface of a pond when a stone is thrown into 
it. Only a portion of the energy of the magnetic field re- 
turns again to the circuit, Electricity travels at the rate of 
186,400 miles per second, and these waves are also propagated 




imp- 

Up 

^ Local Bttlcn 



Fig. 301. — Connections for Three Telegraph Stations Using Eelays. 
One transmitting wire is used and a ground return. 

at this speed. There are also about 230 million waves 
radiated per second. To propagate these waves with the best 
results from an induction coil, the secondary terminals are 
connected to brass spheres, between which the discharge 
occurs. 

316. Wireless Telegraphy. — In wireless telegraphy sig- 
nals are transmitted through space by electric waves. These 
waves are not obstructed by trees, houses, hills, fog, etc., and 
may be transmitted on land or across water. The S} r stem 
requires a transmitter and a receiver. The transmitter is gen- 



332 



PRACTICAL ELECTRICITY. 



erally an induction coil capable of giving from a 3 to a 6-inch 
spark between brass spherical terminals, the spark gap being 
regulated to obtain the best results for any given conditions. 
One terminal of the secondary is also connected to a vertical 
wire or "mast," which assists in the propagation of the 
waves while the other terminal is grounded, Fig. 302. A 
telegraph key, Fig. 298, is introduced into the primary circuit 
of the induction coil, whereby the " dot " and "dash" 
system of signals may be used. Details of the receiving appa- 
ratus are shown in Fig 302. A small glass tube (say £ inch 
inside diameter) contains two plugs of silver, separated from 
each other by a small gap (about .04 inch), which space is 
partially filled with a mixture of silver and nickel filings, and 
forms what is called the coherer. The plugs are connected in 





Fig. 302.- 



-Connections of Transmitting and Receiving Stations for the Wire- 
less System of Telegraphy. 



The stations may be located miles apart with no metallic connections between them. 

circuit with a battery and a relay of several hundred ohms 
resistance. One plug is also connected to a vertical receiving 
mast, and the other to the ground. The relay is made to close 
a local circuit containing a battery and telegraph sounder, 
Fig. 299. Owing to poor contact between the silver plugs 
and the filings the resistance of the coherer may be 1000 ohms 
or more, so that the battery cannot send sufficient current 
through it to operate the relay, When the coherer is struck 
by an electromagnetic wave, propagated from the distant 
spark coil, just as a chip floating on a pond would be struck 
by a ripple, the filings cohere and lower the resistance of the 
coherer to about 5 ohms. The battery now sends a current 
through it which operates the relay, and the signal trans- 
mitted is reproduced by the sounder. If the coherer be 



THE INDUCTION COIL. 333 

gently tapped the filings will decohere, and their resistance 
become as high as before. This can be automatically ac- 
complished by locating the coherer tube near the sounder 
•armature, so that in reproducing the signal it taps the tube, 
and thus " decoheres " it after each signal. Signor Marconi, 
who first perfected the system, uses an exhausted coherer 
tube with sealed-in electrodes, this being more sensitive, as 
the particles do not become oxidized. Telegraphic commu- 
nication by wireless telegraphy has been established between 
ships at sea and the mainland for a distance of more than 
one hundred miles. The ship and the shore station were 
equipped with duplicate transmitting and receiving instru- 
ments. 

QUESTIONS. 

1. How does an induction coil differ from a primary battery? 

2. What is the difference between the current flowing from a bat- 
tery and that from the secondary of an induction coil ? 

3. The primary of an induction coil is wound with 480 turns of 
wire and the secondary, with 80 turns. If 1200 volts are maintained 
across the primary terminals, what will be the relative voltage across 
the secondary terminals ? 

4. An interrupted current in the primary of an induction coil pro- 
duces an alternating current in the secondary circuit. Explain fully 
how one secondary terminal can then be called a cathode and the 
other an anode. 

5. Make a complete sketch of an induction coil with condenser, 
and indicate the directions of current in primary and secondary cir- 
cuits at " make " and at " break." 

6. What is the advantage of using a condenser with an induction 
coil ? 

7. What is the objection to using a solid iron core in the construc- 
tion of an induction coil ? 

8. Make sketch of Wehnelt interrupter connected to an induc- 
tion coil. Indicate direction of currents. 

9. What is a fluorescing screen and how is it used for practical 
purposes ? 

10. Explain the principle of action in a simple telephone trans- 
mitter. 

11. What is a microphone? 

12. Wh at advantage does a microphone transmi tter possess over that 
of a simple type of transmitter ? 

13. Make complete sketch of a transmitting and receiving telephone 
station using Blake microphone transmitters. 



LESSON XXVI. 



DYNAMO ELECTRIC MACHINES. 

The Dynamo— Classification of Dynamos — A Simple Dynamo — Alter- 
nating Current Dynamo — Graphic Kepresentation of an Alternat- 
ing Current — Magneto Alternator — Simple Direct Current Dy- 
namo — Graphic Representation of a Direct Current — Multi-Coil 
Armatures— Gramme Ring Armature— Induced E. M. F. in a 
Ring Armature— Siemens Drum Armature— Advantages of Drum 
and Ring Armatures — Drum-Wound Ring Armatures — Open 
Coil Armatures— Questions. 

317. The Dynamo.— The dynamo is a machine for con- 
verting mechanical energy into electrical energy by means of 
electromagnetic induction. A dynamo does not create elec- 
tricity, but generates 
or produces an induced 
electromotive force, 
which causes a current 
to flow through a prop- 
erly insulated system 
of electrical conductors 
external to it. The 
amount of electricity 
obtainable from such a 
generator is dependent 
upon the mechanical 
energy supplied. In 
the circuit external to a 
dynamo the E. M. F. 
causes the electricity to 
flow from a higher or 
positive potential to a 
lower or negative potential, just as water flows from a higher 
to a lower level. In the internal circuit of a dynamo the 
E. M. F. causes the current to flow from a lower potential to 
a higher potential, just as water is pumped or forced from a 
lower to a higher level. The action of a dynamo is based upon 
334 




Fig. 303.— Bipolar Dynamo or Motor. 



DYNAMO ELECTRIC MACHINES. 



335 




Fig. 304. — Dissected Bipolar Dynamo. 



LIST OF PARTS. 

F-Frame. A- Armature. C-Commutator. C-Field coil complete. P-Part. 

B-Brush. W-Screws. 



FRAME-F. 

Base, 

Field magnet, 
Pillow blk., lower 

part, 
Pillow blk., lower 

part comra. end, 
Pillow blk., cap, 
Rocker arm, 
Binding post saddle, 
Journal box, 
Oil rings, 
Oil rings retaining 

lips, 
Pulley, 



Part. 



3K 

4 

5 



F 9 
F10 



Armature, complete, A 

Commutator, com- 
plete, M 

Field coils, complete, C 



PARTS-P. 

Name-plate, 

B. posts studs, 

" " nuts, 
" labels, 
" insulation, 
" cable tips, 

Rocker arm cable tips, 

Flexible cables, 

Rocker arm handle, 

BRUSHES-B. 

Brush holder, 
Brushes, 
Brush holder, 

" " pressure 

plate, 
Brush holder thumb- 
screw, 
Brush holder springs, 
" " spring 
tightener screw, 
Brush holder collars, 
" " rod nuts, 
" " rod, 



Part. 
P 1 
P 7 
P 8 
P 8^ 
P 9 



P10 
Pll 
P 13 
P14 

B 

B 1 
B 3 



B 5 
B 6 



b oy 2 

B 7 

B 8 

B 9 



parts-p. Part. 
Brush holder rod in- 
sulation, B 10 

SCREWS-W. 

Field to base, 
Pillow blk. to base, 
Cap to pillow blk., 
Oil ring lip, 
Rocker arm set screws 
Rocker arm handle, 
Comm. set screws, 
Name-plate to field, 
Pulley set screws, 
Wing nuts, 
Brush spring to holder, W 16 
" pressure plate to 

holder, W 17 

Saddle to field, W 18 

Screw pin in journal 

box, 
Oil chamber cover, 
" '" stopper 

screw, 



W 1 
W 2 
W 3 
W 5 
W 6 
W 7 
W 8 
W12 
W13 
W14 



W23 
W24 



W25 



336 PRACTICAL ELECTRICITY. 

the principles of electromagnetic induction, discovered by 
Faraday, and fully considered in Lesson XXIV. 

The dynamo consists essentially of two parts : a magnetic 
field, produced by electromagnets, and a number of loops or 
coils of wire wound upon an iron core, forming the armature, 
and so arranged that the number of the magnetic lines of force 
of the field threading through these coils will be constantly 
varied, thereby producing a continuous E. M. F. 

318. Classification of Dynamos. — According to their 
mechanical arrangement, dynamos may be divided into three 
classes : 

1. A stationary field magnet and a revolving armature, 

2. A stationary armature and a revolving field magnet, 

S. A stationary armature and a stationary field magnet, between 
which is revolved an iron core. 

In the first class provision is made for conducting the cur- 
rent from the armature either by collector rings, ^[ 320, or by 
a commutator, ^[ 323. In the second class provision is made 
for conducting the current to the revolving field by collector 
rings, while in the third class there are no moving wires nor 
contacts. Dynamos may be further classified according to 
their design and mechanical construction into, 

1. Direct current machines, 

2. Alternating current machines, or alternators. 

In direct current dynamos the field magnets are usually 
stationary while the armature revolves ; in alternators, the 
armature is usually stationary while the field magnets revolve, 
while in some types both are stationary while an iron core is 
revolved. All dynamos are practically alternators — that is, 
machines in which alternating currents are generated. When 
provided with a suitable commutator, ^[ 323, the current is 
made direct in the external circuit, but still alternates in the 
machine. 

319. A Simple Dynamo. — Consider the single closed loop 
of wire, ABCD, Figs. 305 and 306, which is mounted on a 
shaft and may be rotated around its horizontal axis in the 
uniform magnetic field, NS, in the direction of the arrow. 
The direction and variation in magnitude of the induced E. M. 
F. is the same as that given under Faraday's Law for the dif- 
ferent positions of a loop during a complete revolution in Fig. 



DYNAMO ELECTRIC MACHINES. 



337 




Fig. 305.— Generation of an E. M. F. 
by the Rotation of Rectangular 
Coils of Wire in a Mag- 
netic Field. 
The field magnets are excited from a 
source of current and the terminals of 
the coil are connected by brushes 
and lead wires to a voltmeter. 



274 and % 291.* At the position ABCD, Fig 306, there is 
no induced E. M. F. in the loop, since all the lines of force of 
the field thread through it. During the first quarter of a rev- 
olution, the lines of force 
threading through the loop are 
gradually diminished at an in- 
creasing rate, and the E. M. F., 
depending on the rate of change 
of the lines of force through it, 
increases in magnitude with its 
direction from b to a in the 
right-hand side of the loop, and 
from c to d in the left-hand 
side. At the position of one- 
quarter revolution, indicated 
by abed, the plane of the loop 
is parallel to the lines of force 
so that none thread through it, 
and the arrows indicate the 
direction of the current. The 
rate of change is now a maxi- 
mum as is also the E. M. F. 

During the second quarter of the revolution the lines of 
force thread through the opposite side, which is equivalent to 
-b,w.o„ a further diminution of the lines 

of force through it, the rate of 
change and the E. M. F. decreas- 
ing until at half revolution the 
E. M. F. is zero. The direction of 
the E. M. F. is the same through- 
out this half revolution, and the 
current flows around the loop 
from a to c, to d, to b, to a, 
changing in strength with every 
variation of the generated E. M. F. 
During the next half revolution the 
same variations in E. M. F. occur 
but the induced E. M. F. is in the 
opposite direction. The current is therefore reversed twice in 
every revolution, or an alternating current flows around the loop. 

* The student is advised to read again If 291 which fully explains the fundamental 
principle of the dynamo. 

22 




Fig. 306. — Direction and Magni 

tude of the Induced E. M. F. 

in a Dynamo. 



338 



PRACTICAL ELECTRICITY. 



320. Alternating Current Dynamo. — To utilize the cur- 
rent flowing in the above closed loop when it is rotated in the 
magnetic field, some mechanical device must be used to lead 
or collect the current from the rotating loop so that it will 
flow through a circuit external to it. Two collector rings are 
used for this purpose and consist of rings of copper mounted 
on a wooden or hard rubber hub, Fig. 307, this being mounted 
on the shaft with the loop. The rings are insulated from each" 
other and from the shaft. The terminals of the loop are con- 
nected, one to each ring, and stationary strips of copper, P 
and M, termed brushes, rest upon the rings and are connected 

to the external circuit. 
When the loop is re- 
volved a sliding or 
wiping contact is thus 
established and the 
current is conducted to 
the external circuit. 

During the first half 
revolution of the loop, 
ABCD, Fig. 307, the 
direction of current in 
AB is from B toward 
A, and from brush, M, 
which is therefore posi- 
tive to the external cir- 
cuit, composed of in- 
candescent lamps in 
parallel. From the 
lamp terminals the 
current flows back to 
brush P, the negative 
brush, and around the loop from C to D, to B, etc. Now con- 
sider the second half revolution, Fig. 308. The direction of 
current in the wires AB, and CD, is reversed, Fleming's rule, 
and current flows from D to C, through brush P, now positive, 
then through the lamps in the opposite direction to that in 
Fig. 307, and through brush M, now negative, to AB, to D, 
etc. In every revolution the polarity of the brushes changes 
twice, or there are two alternations of current per revolution in 
the external circuit. The number of alternations per minute in 
any alternator equals the speed in revolutions per minute mul- 




JLANLPS 



Fig. 307. — Simple Alternating Current Dynamo. 

At the instant depicted in the revolution 
brush M is positive. 



DYNAMO ELECTRIC MACHINES. 



339 



tiplied by the number of poles. The number of times which 
the alternations occur is usually expressed simply as the fre- 
quency, thus, a frequency of 7200 alternations per minute 
means 7200 reversals of current. The frequency is usually 
expressed for the period of one minute. 

Student's Experimental Dynamo and Motor.— A simple appa- 
ratus for studying the principles of induction and commutation in a 
dynamo, is illustrated in Fig. 309, and consists of a horseshoe electro- 
magnet fitted with cast-iron pole pieces and mounted on a wooden 
base. A rectangular coil of No. 26 copper wire is mounted on a hard- 
wood sbaft, provided with 
pointed steel ends and sus- 
pended between two brass V 
centres, suitably supported 
by a brass framework ex- 
tending from the pole pieces. 
The framework also carries 
two insulated brush holders. 
At one end of the shaft the 
coil terminals are connected 
to a pair of collector rings 
mounted upon it, while the 
same terminals are also con- 
nected to a two-part com- 
mutator at the other end of 
the shaft. By reversing the 
position of the coil between 
the pole pieces the brushes 
will rest either upon the 
rings or upon the commuta- 
tor. The electromagnets 
have a resistance of 1.3 ohms 
each and are to be excited 
from a source of current. 
The brushes may be con- 
nected to a detector galva- 
nometer, and when the shaft 
is rotated by hand either the 
alternating or direct current 
may be studied. The resistance of the rectangular coil is 5 ohms. 
When connected as a shunt motor the rectangular coil will make 
several hundred revolutions with an applied E. M. F. of 4 volts. 

Exp. 91 : Separately excite the magnets (connected in series) of the 
student's experimental dynamo, Fig. 309, so that one pole piece will 
be N and the other S, and adjust the brushes so that they will bear 
lightly upon the collector rings. Connect the brushes to the detector 
galvanometer, Fig. 153. 

(a) Revolve the shaft slowly and note the alternating deflection of 
the galvanometer needle. 

(b) Increase the speed and note that the needle remains at zero 
with a perceptible vibration. 




Fig. 308. — Simple Alternating Current 
Dynamo. 

Direction of current in the coil at one-half 

revolution from the position in Fig. 307. 

Brush M is now negative. 



340 



PRACTICAL ELECTRICITY. 



(c) Turn the coil to the vertical position, break the field circuit, 
and note the galvanometer deflection ; make the field and again note 
the deflection. Why are the deflections opposite ? 

(d) Reverse the polarity of the fields and repeat (c), noting results. 

(e) Turn the coil so that 

it is horizontal ; make 
and break the circuit as 
in (c). The galvanometer 
needle is not appreciably 
deflected. Why is this 
so, since it was stated that 
this was the maximum 
position of induction of 
a loop rotated in a bipolar 
field ? Why is it different 
in each case ? 

321. Graphic Rep- 
resentation of an Al- 
ternating Current. — 

The changes in direc- 
tion and magnitude 
of an alternating cur- 
rent are usually repre- 
sented diagramati- 
cally. For example, 
suppose an alternating 
current of 5 amperes 
to flow for one second 
in a positive direction, and then be automatically reversed 
and flow for one second in the opposite or negative direction, 
and reversed again, this cycle of events continuing at regular 
intervals while 
the current flows. 
The action is rep- 
resented in Fig. 
310, where the 
horizontal line, 
P K, is divided 
into equal dis- 
tances, PC, CF, 
FK, etc., repre- 




309. — Student's Experimental Dynamo 
and Motor. 




Fig. 310. — Graphical Representation of an 
Alternating Current. 



sen ting intervals of time. The vertical line, AM, at right 
angles to it is divided into distances representing units of 
current, the current being in a positive direction when indi- 
cated above PK, and negative, when below PK. When the 



DYNAMO ELECTRIC MACHINES. 



341 



switch is closed the current immediately rises to its full 
strength of 5 amperes, or from P to A, and 5 amperes are 
maintained constant in a positive direction for one second, 
A to B. When point B is reached at the end of the first 
second the current falls abruptly to zero, B to C, and rises to 
5 amperes in a negative direction, and is maintained for an 
equal interval of time, D to E, when it again falls to zero, at 
F, and repeats the same cycle of events in equal intervals 
of time. The line 
PABCDEFGHK is 
called the current wave. 
In Fig. 310 the cur- 
rent is depicted as 
being of constant 
strength during each 
second, while it was 
shown in ^ 291 and 
320 that during rota- 
tion of the loop the 




Fig. 311. 



-Graphical Representation of an 
Alternating Current. 



current and E. M. F. varied. This 
variation in magnitude is represented in Fig. 311, which is 
constructed similar to Fig. 310, but the current gradually 
rises to its maximum value of 5 amperes, P to A, and as 
gradually diminishes again to zero, A to B, during the first 
second, which may also represent one-half revolution of the 
loop. Corresponding with the second half revolution, the 

current gradually 
rises from B, reach- 
ing its maximum 
negative value at C 
(three-quarter rev- 
olution), and fall- 
ing again to zero at 
D, and so on. In 
an alternating cur- 
rent dynamo the 
alternating current wave is not so abrupt as that depicted in 
Fig. 311, but more truly represented by the undulatory curve, 
Fig. 312, which represents the same variations as before. 
Thus at the end of one-half second the current reaches its 
maximum value, 5 amperes, represented to scale by the line 
AG, while the value of the current at one-quarter second is 
equal to the line LK, or about 3 amperes. 




Fig. 312. — Graphical Representation of an Alter- 
nating Current. 



342 



PRACTICAL ELECTRICITY. 



322. Magneto Alternator.— The E. M. F. of a dynamo 
depends upon, 

(a) The number of lines of force cut by the armature wires, 

(b) The number of cutting wires, 

(c) The speed at which the lines of force are cut. 

The E. M. F. of the single loop armature, Fig. 308, will 
therefore be increased by winding it upon an iron core called 
the armature core, as in Fig. 313, which greatly increases the 
number of lines of force between the poles N and S, and also 
by winding a great many turns in the same 
direction around this core. Fig. 313 
illustrates a Siemens shuttle armature, 
which is revolved between the poles of 




Fig. 313.— Siemens 
Shuttle Armature. 



Cross-section of 
Shuttle Armature. 




Fig. 314— Single Ar- 
mature Coil with 
Two-part Com- 
mutator. 



the permanent magnets, NS, and called a 

magneto generator, because the field is 

produced by permanent magnets. Only 

one turn is illustrated, but the shuttle is 

filled with wire, as in the cross-sectional 

view. This construction is only employed in small 

machines, Fig. 318, such as those used for magneto telephone 

call systems, and magnetos used in testing insulation of lines, 

U 256. In dynamos for generating large currents, a stronger 

field must be employed and the armature core laminated to 

prevent excessive loss of energy by eddy currents, etc. 

323. Simple Direct Current Dynamo. — When it is de- 
sired to have the current from a generator flow always in one 
direction in the external circuit, like a battery current, for 
such purposes as charging accumulators, electroplating, etc., 



DYNAMO ELECTRIC MACHINES. 



343 




a commutator must be substituted for the collector rings in the 

simple alternator of Fig. 308. The function of a commutator 

is to reverse or commute the alternating current of a dynamo at 
the proper instant in each revolution before it 
flows through the external circuit. A two-part 
commutator, connected to the single loop, is 
shown in Fig. 314. It is practically a split ring, 
mounted upon a hub insulated from the shaft, 
with the parts of the ring also insulated from 
Fig. 315.— Sec- each other, as shown in the section, Fig. 315. 

tion of Two-Part Brushes rest upon the split ring at diametri- 
cally opposite points. The connections of a 

simple direct current dynamo are illustrated in Figs. 316 and 

317, from which the act of commutation can be studied. In 

Fig. 316 the wire AB is rotated down past the S-pole. The 

direction of current is 

from B to A, by Fleming's 

rule, and to the external 

circuit by brush M, which 

is positive ; then from the 

lamps to the negative 

brush and around the 

loop, CDBA. When the 

loop is rotated one-half 

revolution, Fig. 317, AB 

is now moving up past 

the N-pole and the di- 
rection of current in it is 

reversed. Its terminal, 

however, is not now in 

contact with brush M, as 

before, but connected to 

brush P. Current flows 

to the external circuit 

from the brush M, which 

is still positive, though the 

current in the armature 

has been reversed, as in 

an alternator. Brush M 




4MF>S 



Fig. 316.— Simple Direct Current Dynamo. 

At the instant, depicted in the revolution 
brush M is positive. 



is consequently always positive and brush P always negative, 
or the current in the external circuit is a direct current flowing 
in one direction only. 



344 



PRACTICAL ELECTRICITY. 



The act of commutation occurs at the instant when the 
wire, moving down past the S-pole, commences to move up 
past the N-pole, either terminal of the coil being connected 

with one brush for one- 
half revolution and 
with the other brush 
for the other half of 
the revolution. With 
a two-part commuta- 
tor, the current in the 
external circuit is in- 
terrupted twice in each 
revolution. A single 
coil armature of this 
type is shown in Fig. 
319, where the arma- 
ture core is omitted. 
The direction of the 
current is indicated by 
the arrows in Fig. 320, 
when the coil is ro- 
tated clockwise, as 
viewed from the com- 
mutator end. 
Fig. 317.— Simple Direct Current Dynamo. _ 

Exp. 92 : Make the 
same connections for the 
student's experimental 
dynamo as given in Exp. 
91, page 339. Adjust the brushes so that they bear lightly upon 
diametrically opposite points of the two-part commutator. 

(a) Upon revolving the shaft slowly the needle is now deflected 
to one side of the zero mark. 

(b) Reverse the direction 
of rotation, and the direction 
of deflection (or polarity of 
the brushes) is now reversed. 

(c) Increase the speed 
and the deflection increases. 
Why? 

(d) Increase the field 
strength by grouping the 
magnet coils in parallel, so 
that the poles w T ill be N and 
S, and the deflection is 
greater when the speed is 
the same as before. Why ? 




Direction of current in the coil at one-half 

revolution from the position in Fig. 316. 

Brush M is positive as before. 




Fig. 318.— Magneto Dynamo. 



DYNAMO ELECTRIC MACHINES. 



345 




Fig. 319.— Single Coil Armature 
With Many Turns. 



Exp. 93 : (a) Repeat Exp. 78, page 297, to determine the direction 
the galvanometer needle deflects for a given direction of current. 

(b) Test with a compass and mark the polarity of the pole pieces. 

(c) Determine, with the aid of the galvanometer, the positive brush 
for a particular direction of rotation. 

(d) Apply Fleming's rule, fl 278, and note whether the polarity 
determined by this method agrees with that already determined. 

(e) Reverse the polarity of the 
fields and again prove Fleming's 
rule. 

324. Graphic Representa- 
tion of a Direct Current. — 

The same method is applicable 
for illustrating the direction 
and magnitude of a direct cur- 
rent as given in ^J 321 for an 
alternating current. Since 
there is no reversal of current in the external circuit, the 
curve will lie above the time line, Fig. 321, and represent 
the magnitude of E. M. F. or current at each instant during 
the rotation of the loop in the two-pole field. The curve 

indicates a pulsating cur- 
rent flowing always in 
one direction. 

325. Multi-Coil Ar- 
matures. — With an ar- 
mature wound with a 
single coil of wire the 
current in the external 
circuit is very pulsating 
as the coil passes through 
the various phases of in- 
duction represented by 
the curve in Fig. 321. 
Fig. 320.— The Induced E. M. F. of Each 111 Fig. 306, consider 

two coils to be placed 
at right angles to each 
other, when, at the instant shown, the current in the 
vertical coil will be zero, while that in the horizontal coil 
will be a maximum. As rotation is continued the current 
in the one coil, ABCD, increases as. that in the other, abed, de- 
creases until, at quarter revolution, current in coil A is maxi- 
mum and in coil a, zero, and so on. There will thus always 




Turn is in Series With Every 
Other Turn. 



346 



PRACTICAL ELECTRICITY. 




Fig. 321.- 



-Graphical Representation of a 
Direct Current. 



be current flowing in one of the two coils, so that if they are 
properly joined to an external circuit the current will be less 
pulsating than when a single coil is used. This is depicted 
in the current curve of Fig. 322, where the solid modulatory 
line represents the pulsating character of the current pro- 
duced by the two coils 
acting together in the 
same circuit. The cur- 
rent is thus never zero 
in the line as in the 
curve in Fig. 321. 
The armatures of dy- 
namos are wound with many coils of wire, so that the current 
may be continuous in the external circuit. 

326. Gramme Ring Armature. — A four-coil direct cur- 
rent Gramme ring armature is illustrated in Fig. 323. The 
ring is made of a number of 
laminated sheets of soft iron g*- 
and the coils wound upon it. « z ■ 
The ending of each coil is 5 i ZJ — lL. 
joined to the beginning of the r — ' ^ ev 

adjacent coil, SO that the Fig. 322.— Graphical Representation 
Winding forms a Complete of a Direct Current. 

closed circuit, or the coils are all in series. At the junction 
of each coil with its neighbor a lead wire is run to a com- 
mutator section, so that instead of the former two-part com- 
mutator one with four sections is now used. As the number 

of coils is increased the commutator 
sections are increased, as will be 
noted in the armatures depicted in 
Figs. 324, 325, and 329. An eight- 
coil ring armature is depicted in 
Fig. 324, rotating against the hands 
of a clock in a bipolar field. The 
connections are the same as those 
given above. The direction of cur- 
rent in the two halves of the ring 
is indicated by arrows and is found 
by Fleming's rule. 
When the external circuit is closed the induced current 
flows in both halves of the winding toward the upper or 
positive brush, and returns from the external circuit to the 



J? !*S jc£ v'r hV 

W Revolution. J 




Fig. 323.— Four-Coil Gramme 

Ring Direct Current 

Armature. 



DYNAMO ELECTRIC MACHINES. 



347 




lower or negative brush, circulating up again through each 
half of the armature. The windings in the halves of the 
armature are in parallel with the brushes. As each coil passes 
from under the influence of the N-pole and comes into 
action under the S-pole, commutation takes place and the 
direction of current 



through it is reversed, 
as will be seen from 
tracing the direction 
of the currents in the 
two upper coils, which 
are opposed to each 
other. The brush is 
located at this point of 
opposition and serves 
to conduct the current 
from both halves of 
the ring to the external 
circuit. The brushes 
resting upon two ad- Fi S- 324.— Eight-Coil Gramme King Direct 
j. i hi xi Current Armature. 

jacent bars will thus 

short-circuit each coil for an instant as it passes from pole to 
pole, and this short-circuiting should occur when there is 
zero E. M. F. in the coil, or at that instant when the mag- 
netic lines threading through it are a maximum, which will 

be when its plane is at right 
angles to the lines of force 
threading through the iron 
ring. The act of commuta- 
tion is further described in 
«|j 338 and Fig. 351. 

327. Induced E. M. F. 
in a Ring Armature. — The 
upper and lower coils in the 
right-hand half of the ring 
Fig. 325.— Multi-Coil Gramme Ring armature, Fig. 324, will have 
Direct Current Armature. about the same E. M. F. in- 

Smooth core pattern. duced in themj gay 2 volts 

each, while the two coils between them will have a higher 
E. M. F. at the same instant, say 4 volts each, since they 
occupy nearly the position of the maximum rate of change 
of the lines threading through them. The total E. M. F. 




348 



PRACTICAL ELECTRICITY. 



of this half of the ring, since these four coils are in series, 
will therefore be 2 + 4 + 4 + 2 or 12 volts, and since 
similar induction takes place in the other half of the ring at 
the same instant, there will be a total of 12 volts induced in 
it. The windings of the two halves being in parallel, the 
E. M. F. at the brushes will also be 12 volts, just as' though 
each half represented a cell of 12 volts E. M. F. and the two 

cells were placed in parallel. The 
current in the external circuit 
will be the sum of the currents in 
each half of the windings. If it 
is 10 amperes, 5 amperes will 



£ Volts 



2 Volts 



<r •» 



1 



\ V) 




w!k%^ 



Vo>+S 



„ 12 Volte flow through each half of the 
ring. The adding together of the 
E. M. F.'s in the coils, and the 
current flowing from them, may 
jL be understood from the following 
Fig. 326.— Battery Analogy of battery analogy. In Fig. 326, 
Induced E.M.F. in a Ring e i g ht cells represent the above 

armature coils and are connected 
4 in series and 2 groups in parallel. The E. M. F. across the 
lead wires is 12 volts, and with 10 amperes in the external 
circuit 5 amperes flow through each group of cells. The 
E. M. F. of one group of cells is the sum of the E. M. F.'s of the 
cells connected in series in that group, or 2 + 4 + 4 + 2 = 12 
volts, and the E. M. F. of 2 groups in parallel is 12 volts. 
If 10 amperes flow through the external circuit, 5 amperes 
will flow through each group 
of cells. 

By employing 8 coils on 
this ring armature the current 
is less pulsating than in the 
four-coil armature, Fig. 323, 
and is represented by the wave 
in Fig. 327. As the armature 
coils are further increased, the wave becomes more nearly a 
straight line, but there will always be a slight pulsation of 
the current. 

Prob. 118 : The joint resistance of the two halves of an 8-pole ring 
armature is .5 ohm. This is called the armature resistance and would 
be measured between the brushes. What is the resistance of the wire 
upon the armature ? 



'fYlYTYTYTYIYfa 



nEVOLWBION 

Fig. 327.— Direct Current Wave of 
a Multi-Coil Armature. 



DYNAMO ELECTRIC MACHINES. 349 

By Formula (45) E = J. R. X nq = .5 X 2 = 1 ohm. 
J. R. = 0.5 ohm, nq = 2 halves in parallel. 
R — resistance of one-half the armature, therefore the total resist- 
ance of the wire upon it = 1 X 2 = 2 ohms. 

The resistance of the armature winding is thus four times the joint 
resistance from brush to brush in this type of armature. 

Prob. 119: The resistance of the eight coils, in series, upon the 
ring armature, Fig. 324, is 4 ohms, what is the armature resistance from 
brush to brush? 

The resistance of one-half of the armature is 4 -*- 2 = 2 ohms. The 
joint resistance of the two halves in parallel is, 

2 
By Formula (43) 2 = 1 ohm. 

The resistance of the wire upon this ring armature is therefore four 
times its joint resistance. 

Prob. 120 : The E. M. F. generated by the ring armature in Fig. 
324 is 12 volts, the armature resistance 1 ohm, an incandescent lamp 
connected to the brushes 2 ohms, leads to lamp 1 ohm. AVhat cur- 
rent will the lamp receive ? See Fig. 328. 
F 12 

By Formula (31 ) C — R , = 2 -i-14-l = 3 am P eres - 

R = 2 + 1 = 3 ohms, E = 12 volts, r = 1 ohm. 
Prob. 121 : What potential will a voltmeter indicate when placed 
across the brushes in Prob. 120? See Fig. 328. 
By Formula (29) E = CxR = 3X (2 + 1) =9 volts. 

C = 3 amperes, R = 2 -f- 1 = 3 ohms. 
The pressure required to send 3 amperes through the armature 
will beE = CXr = 3xl = 3 volts, or 12 — 9 == 3 volts. 

By substituting a pair of collector rings for the commuta- 
tor, the ring armature of Fig. 324 will give an alternating cur- 
rent to the external circuit. The winding is the same but 
only two lead 
wires are taken \vbits 
from the coils, at 




points diametn- ^P : ; — p— 7 

r n ., J2Z Leads r-oh-m. 

cally opposite fgv i-ohm 

and connected (£*^~r om ■ 2,-oli-ms 

one to each col- ]^lL 3- amperes. 

lector ring. With Fig 328 ._e. M. F. and P. D. of an Armature, 
the increased 

number of coils the alternating E. M. F. is increased, since the 
E. M. F.'s in the coils at any instant are in unison. The com- 
mutator and collector rings may both be mounted on the 
same armature shaft, when the machine will give either a 
direct or alternating current, or both, at the same time to two 



350 



PRACTICAL ELECTRICITY. 



independent circuits. The dynamo would then be called a 
double current generator. The collector rings would be con- 
nected one to each diametrically opposite section of the com- 
mutator ; for example, 1 and 5 in Fig. 324. 

328. Siemens Drum Armature. — Instead of winding the 
armature coils upon a laminated ring, they are sometimes 




Fig. 329. 



-Multi-Coil Siemens Drum Armature. 
Tooth-core pattern. 



wound upon a cylindrical laminated iron core made by as- 
sembling, upon the armature shaft, thin sheets of soft iron ; 
after being properly insulated the coils are wound upon the 
core, and connected in series and to the commutator in the 

same manner as that given for 
the ring armature. Fig. 330 
depicts a four-coil Siemens 
drum armature with its com- 
mutator, suitable for a bipolar 
field. In practice a great 
many coils are wound upon 
the core covering its entire 
area, the commutator sections 
increasing with the sub- 
division of the armature coils. 
The induced E. M. F. in that 
part of a coil under one pole is 
in the opposite direction to 
that in the other half of the 
coil so that the two E. M. F.'s are in series, as in two consecu- 
tive coils in the ring armature. Both halves of the drum 
armature coils are in parallel with the external circuit so that 




Fig. 330. 



■Four-Coil Siemens Drum 
Armature. 



DYNAMO ELECTRIC MACHINES. 



351 



the induced E. M. F. is that generated by one-half of 
the total conductors upon the core, and each half of the wind- 
ings deliver one-half of the total current flowing to the ex- 
ternal circuit. 

329. Advantages of Drum and Ring Armatures.— The 
difference between the ring and drum armature is that in the 
former, the active ivire of each coil cutting the magnetic lines 




Fig. 331.— Tooth-Core Armature Body With Two Formed Coils in Position. 

The wound and formed coils are also illustrated. The armature 
is intended for a six-pole field. 



of force is that part located only on the periphery of the ring 
while that on the ends and inside of the ring cuts no lines of 
force, and is termed dead wire. 

This serves only to conduct currents from one active con- 
ductor to the next. In the drum type there is less dead 
wire, since each half of the coil cuts magnetic lines of force, 
and that on the ends of the core is only inactive and serves 



352 PRACTICAL ELECTRICITY. 

to connect the active conductors. The C 2 R loss in a ring 
winding will thus be greater than in a drum armature of the 
same capacity. On the other hand, in ring armatures the 
coils can be much better insulated from each other, and are 
more readily accessible for repairs than in the drum armature. 
For these reasons high voltage direct current arc lighting 
dynamos are generally constructed with ring armatures. A 
combination of the drum and ring winding in what are 
known as drum-wound ring armatures is extensively used in 
practice and further described in ^[ 330. 

330. Drum-Wound Ring Armatures. — Some of the ad- 
vantages of both the drum and ring windings are obtained by 
using a slotted laminated ring armature core and winding the 
wire, drum fashion, upon this ring, Fig. 331. 

There are thus two active conductors for each coil, as in 
the drum type, and the width of the coils is such that when 
one of these conductors is passing under a N-pole the other 
passes under a S-pole. The direction of a current will thus 
be opposite in each half of the coil underneath the poles, 
and so flow around the coil in the same direction. Fig. 331 
depicts an armature having a slotted tooth core built up from 
punchings of thin sheet iron and held in position by two 
flanged iron rings securely fastened to the spider arms, as 
shown. The coils are first wound, then properly shaped 
upon formers, removed, wrapped with insulation, varnished 
and baked, and then placed in the slots of the armature 
core. The winding is held down by clamps at each end 
and the coil terminals properly connected to the commuta- 
tor. The coils shown are intended for a six-pole field, which 
is practically three bipolar fields, and constitute a multipolar 
field, ^[ 346. In some types of large size dynamos, solid 
copper bars, properly insulated, varnished, baked, etc., are 
placed in the armature slots, which are lined with mica 
formed tubes. The bars are then connected by flexible 
formed terminals, according to the method of winding. 

331. Open-Coil Armatures. — The armatures previously 
described are called closed coil armatures, because the coils are 
all connected, forming a closed winding around the armature. 
When very high potentials are to be generated, as, for exam- 
ple, 8000 volts for a series constant current arc-lighting cir- 
cuit, ^[ 348, the closed coil winding is not as suitable, since 
the potential difference between adjacent commutator bars 



DYNAMO ELECTRIC MACHINES. 



353 




Fig. 



Open-Coil Armature. 



becomes very high, and may jump or " flash " from bar to 
bar, or even from brush to brush. Open coil armatures are 
designed to obviate this difficulty, and are used principally 
for arc lighting. * A simple form of open coil armature is 
depicted in Fig. 332. Two coils, A,B, wound at opposite 
positions on the ring core are connected in series, and the 
two remaining terminals to two diametrically opposite com- 
mutator bars, 1,2. Another set 
of two coils, C,D, are wound in a 
position at right angles to the 
former coils, connected two in 
series, and to two independent 
diametrically opposite bars, 3 
and 4. At a particular instant 
of revolution, shown in Fig. 332, 
the coils C and D have the 
maximum E. M. F. induced in 
them, and are connected to the 
external circuit by the brushes, while coils A and B are in the 
position of zero induction and out of circuit at this instant. 
An instant later coils A and B w T ill be in the active position 
and connected to the circuit with coils C and D cut out. Two 
independent two-part commutators are used instead of that 
shown in Fig. 332 and placed side by side, Fig. 333, one set 
overlapping the other. The brush is made equal to the wddth 
of both sets of bars, and by this arrangement 
the external circuit is not broken each time 
a pair of coils is switched out of circuit. 
With the four-coil armature the current 
would be very pulsating in the external cir- 
cuit, so that more coils are used in practice 
and more commutator segments, or several 
commutators similar to Fig. 333, placed side 
by side on a shaft, and their respective 
brushes connected in series or parallel with 
the external circuit, so as to obtain the maximum inductive 
effect of all the active coils. For example, the open-coil 
armature of a 160-light Brush arc generator is wound 
with 32 bobbins, and at one instant of revolution there 

*In Brush and Thomson-Houston direct current arc-light generators and in Westing- 
house alternating current arc generators. The Wood, Excelsior, and Western Electric 
dynamos are closed coil ring armatures, subdivided into a great many sections to reduce 
the potential between adjacent commutator bars. 

23 




Fig. 333— Com- 
mutator for an 
Open-Coil Arma- 
ture. 



354 PRACTICAL ELECTRICITY. 

are 2 sets of 4 coils each in series ; 2 sets of 4 coils each 
in series, with 2 groups in parallel, and 2 sets of 4 bobbins 
each out of circuit. The E. M. F. generated by this arma- 
ture is 8000 volts. 

QUESTIONS. 

1. How does a dynamo differ from a primary battery ? 

2. Give three classifications of dynamos according to their mechani- 
cal construction. 

3. How does an alternator differ from a direct current dynamo ? 

4. Sketch four positions of a single rectangular coil of wire at each 
quarter of a revolution when rotated in a bipolar field, the terminals 
of the coil being provided with two collector rings. Indicate polari- 
ties and direction of current in the internal and external circuits in 
each sketch. 

5. Make sketches when the terminals of the coil in question 4 are 
connected to a two-part commutator. 

6. The armature of a dynamo revolving at 1000 revolutions gene- 
rates 110 volts. State three ways in which you can increase the 
voltage. 

7. What is the difference between a drum, a ring, and a drum- 
wound ring armature ? State the advantages of each. 

8. What is the advantage of open-coil armatures over the closed- 
coil type ? 

9. Make sketch of a 12-coil direct current bipolar ring armature 
with two turns per coil ; indicate direction of current in the armature 
and external circuit. 

10. The resistance of the wire wound upon a bipolar ring armature 
is 20 ohms. What is the armature resistance ? Ans. 5 ohms. 

11. The armature in question 10 generates an E. M. F. of 50 volts. 
What current will flow through some lamps joined in parallel with it 
having a joint resistance of 4 ohms ; resistance of lead wires 1 ohm? 
Ans. 5 amperes. 

12. What will be the P. D. indicated by a voltmeter, in question 11, 
when placed (1) Across the lamps? (2) Across the brushes ? Ans. 
(1) 20 volts; (2) 25 volta. 






LESSON XXVII. 



ARMATURES. 

Armature Core Construction — The Commutator and Brushes— Arma- 
ture Core Insulation — Table XXL Insulation Test — Armature 
Winding — Armature Core Loss-Hysteresis — Armature Reactions 
— The Act of Commutation of an Armature Coil-Sparking at the 
Brushes— Position of the Brushes— Causes of Sparking — Capacity 
of a Dynamo— Commercial Rating of Dynamos — Losses in a 
Dynamo — Efficiency of a Dynamo — Questions. 

332. Armature Core Construction — Eddy Current Loss. — 
The armature core which is introduced into the magnetic 
circuit to lower its reluctance, is an electrical conductor also, 
and when rotated in the magnetic field will have currents in- 
duced in it, according to the principles of electromagnetic in- 
duction. A certain 
portion of the 
energy driving the 
armature is thus 
expended in pro- 
ducing useless elec- 
tric currents, eddy 
currents, ^f 292, in 
the core, and which 
do not appear in the 
external circuit ; 
this is termed eddy 

current loss, and con- . 
... , » .-. Fig. 334. — Eddy Currents in the Armature Core. 

stitutes one ot the 

internal losses of a dynamo. A section of a solid armature 
core is illustrated in Fig. 334, and the direction of the in- 
duced eddy currents (found by Fleming's Rule, ^| 278), 
indicated at this particular position of the armature core in 
the course of its revolution. The heat produced by these 
currents is chiefly at the outer surface of the core, where 
the eddies are strongest. The armature wires being wound 
on the surface will also be heated and their resistance in- 

355 




356 



PRACTICAL ELECTRICITY. 




Fig. 335 —Sheet 

Iron Armature 

Core Disc. 

.015-inch thick. 



creased, and as a result the C 2 R loss will be increased. There 

are thus two evil effects of the eddy currents. 

Eddy current losses may be considerably diminished by 

building the armature up of a series of thin discs of soft sheet 

iron or steel, the surfaces of which have been allowed to ox- 
idize (rust), thus introducing an insulator 
between the sheets, which decreases the 
electrical conducting power of the core. 
Sometimes pieces of tissue paper are inter- 
posed between the sheets, or brass discs 
introduced at intervals to break the con- 
tinuity of the circuit, and also to afford 
armature ventilation. A single sheet iron 
punching of a tooth-core ring armature is 
represented in Fig. 335, while the effect of 
lamination is shown in Fig. 336, in which 
the eddies are confined to each lamination. 

Only four laminations are purposely shown in the core, in 

Fig. 336, to magnify the effect. The thickness of the metal 

from which they are punched may be .015 inch, so that a great 

man}'- separate pieces are required for a single armature core. 
333. The Commutator and Brushes. — A commutator 

consists of a number of 

bars or segments of 

drop-forged, hard 

drawn copper, assem- 
bled around an iron 

hub and thoroughly 

insulated from the hub 

and from each other, 

Fig. 337 ; mica is used 

for the insulation. The 

bars must be securely 

held in place, since a 

high or low bar would 

cause a break in the 

circuit each time it 

passed under the brush 

and destructive arcing 




Fig. 336. — Laminated Armature Core. 

The thickness of the discs is magnified to show the 
eddy currents. 



would result. A simple method of 
construction is illustrated in Figs. 338, 339, etc. A brass or 
iron hub of the shape shown in the sectional view, Fig. 338, 
drilled to receive the armature shaft, is insulated with a sleeve 






ARMATURES. 



357 




Fig. 337.— Commutator for a 

Direct Current Dynamo 

or Motor. 



and formed collar made of sheet mica, when it is ready for 
the reception of the bars which are forged with grooves in 
the ends, as in Fig. 339. The projecting insulated tongue on 
the hub fits into a corresponding 
groove in a bar, and when all the 
bars are assembled around the hub, 
with strips of mica between each, 
they are locked in place by the pro- 
jecting insulated V-tongue of a 
washer screwed upon the hub and 
backed up by a lock-nut. A partial 
section through the commutator is 
shown in Fig. 340, in which the 
heavy line represents the insulation, 
and from which the manner of locking the bars will be un- 
derstood. A lug extends at right angles from one end of each 
bar to which the armature wire is soldered. 
Carbon brushes, copper plated to decrease 
their resistance, are secured in a brush holder 
and made to press against the commutator by 
spring pressure. Details of the brush holder 
are shown in Figs. 304 and 361. The brush 
holder stud or shaft is securely bolted to, but 
insulated from, the rocker arm', and connected 
by flexible cables to the external circuit. 
The function of the rocker arm is to move 
the position of the brushes upon the com- 
mutator so that the current is led away from 
the armature at the proper point of commu- 
tation. Fixed copper brushes are used upon alternators 
because there is no tendency to spark at the brushes, as in 
direct current machines, and copper is a much better con- 
ductor. In very low voltage dy- 
namos copper brushes are used to 
advantage. 

334. Armature Core Insula- 
tion. — The armature cores of all 
large generators are slotted for 
the reception of the conductors 
and are called tooth-core armatures, Fig. 341. Mica tubes, 
formed by the aid of heat, from sheets built up of many 
thicknesses of mica united by shellac, etc. , are fitted into the 




Fig. 338.— Commu 

tator Hub. 
Made of brass or iron 



f 



Fi< 



339.— Forged Copper Com- 
mutator Bar. 



158 



PRACTICAL ELECTRICITY. 



slots and formed rings or segments of the same material are 
used upon the ends of the cores. The quality of the insulation 
and the care required in insulating increases directly with the 

potential to be developed 

J W^'^j}. by the armature ; an ar- 
M -^ mature wound to develop 
1000 volts requiring a 
HUB better degree of insula- 
tion than one wound for 
only 125 volts. Smooth 
core armature bodies are 
used in some small ma- 
chines and are generally 
wound with several layers 




WASHER 

Fig. 340. — Sectional View of a Commutator. 



of linen or silk, then 
shellaced and baked in 
an oven to drive out all 

moisture. The armature discs are bolted between end flanges, 

the circumference of 

which are slotted for -mi&Jm 

the reception of small 

fibre wedges, which 

serve as guides for 

the coils to be wound 

upon the core, Fig. 

342. The insulation 

is pierced and the 

wedges driven into the 

slots. 

The quality of an 

insulating material is 

tested by subjecting 

it to a high potential and 

the insulation " breaks 




Fig. 341. — Tooth- Core Armature Body 
With Formed Coils in Position. 



down," 




342. — Drum Armature Showing the Method 
of Winding a Coil. 



ascertaining at what voltage 
or conducts, instead 
of insulates. The 
specimen to be 
tested, as a piece o 
paper or fibre, may 
be interposed be- 
tween two plates 
connected to a 
source of high 



i 

7 



ARMATURES. 359 

potential, which is capable of being regulated. The voltage 
is then increased till a spark passes from plate to plate 
through the specimen, thereby puncturing it, as in Exp. 88, 
page 323. The following insulating materials and the vol- 
tages at which they " broke down " under test will give the 
student some idea of what is meant by insulating qualities. 

Table XXI— Insulation Test. 



"Break Down" 


Thickness 




Voltage 


in Inches 




2000 


.013 


ordinary shipping tag 


500 


.010 


soft grey wrapping paper 


800 


.015 


varnished linen 


800 


.016 


white gummed tape 


1500 


.031 


varnished canvas 


2000 


.037 


red sheet fibre 


5000 


.022 


yellow press-board 


6500 


.018 


mica and cheese cloth 


8500 


.035 


grey press-board 



The insulation of electrical machinery is usually tested by 
applying several times the voltage that the apparatus is de- 
signed to stand ; for example, a 1000 volt armature may be 
subjected to 10,000 volts, one terminal of the high potential 
source being connected to the core, and the other to the cop- 
per windings. If there is any defect in the insulation, upon 
application of the high voltage it will readily be noted on 
indicating instruments in the testing circuit. 

335. Armature Winding. — After complete insulation of 
the armature core it is ready to receive the armature wires. 
In large tooth-core bodies the conductors are generally in the 
form of straight bars of rectangular cross-section which have 
been previously insulated. One or more bars are inserted in 
each slot, and the coils formed by connecting their ends to 
other bars by flexible formed end terminals soldered to them, 
provision being made for commutator taps at the ends of the 
proper coils, when the armature is for a direct current machine. 
There are many kinds of armature connections, each de- 
signed for a specific purpose, such as series winding, double 
or triple multiple-winding, multiple- wound two-circuit wind- 
ing, etc.* A small smooth-core drum armature body for a 
two-pole field is depicted in Figs. 342 and 343. Suppose it 

* Armature winding is treated in books relating to dynamo design. 



360 



PRACTICAL ELECTRICITY. 




Fig. 343. — Position of the Coils on a Drum 
Armature. 



is to be wound as a closed coil series wound armature with 8 
coils and 3 turns per coil. The armature core is divided into 
16 divisions by the fibre wedges alluded to in ^j 334, and the 
first coil wound in division 1 and 9 ; the second, in 2 and 10, 
and so on. Commence to wind the beginning of coil No. 1 

in division 1, and it 
will end in division 9, 
Fig. 343 ; commence 
coil No. 2 in division 
2, wind in the same 
direction as coil No. 1, 
and it will end in 
division 10, and so on. 
The coils should then 
be bound to the arma- 
ture core by mounting 
it in the lathe and 
winding several bands around them, each consisting of a 
number of turns of phosphor bronze wire. Mica is interposed 
between the band wires and the armature wires, and the 
former soldered together, thus producing a solid band. A 
commutator with 8 bars will be required since there are 8 coils 
and the coils are to be joined 
in series. Connect the be- 
ginning of coil No. 1 to bar 
1 and the ending of coil No. 
1 to bar 2, Fig. 344 ; the be- 
ginning of coil No. 2 to the 
ending of coil No. 1 at bar 
2 ; the ending of coil No. 2 
to bar 3 and to the beginning 
of coil No. 3, and so on until 
finally the ending of coil 8 
will connect to the be- 
ginning of coil 1 at bar 1. 
The coils are thus all in 

Series around the armature ; Fig. 344.— Connecting the Armature 
the commutator bars form- Coils to the Commutator, 

ing the connecting links between the coils. Many more turns 
could be wound per layer, and more layers per division, to 
increase the induced E. M. F. After the first set of coils is 
wound a second set may be wound on top of them, with 




ARMATURES. 



361 



proper insulation between them ; 16 bars would have been 
required had this method been adopted in Fig. 343. The 
method of varying the winding according to the potential 
desired is illustrated in Fig. 345, which represents the number 
of wires per coil on an 8 H. P. dynamo when it is wound for 
125 volts, as in A ; 250 volts, in B ; 500 volts, in C. The size 
of the wires decreases as the voltage increases, since for the 
same power the current will be less, and the turns increase in 
direct proportion to the voltage, there being 3, 6, and 12 turns 






A b c 

Fig. 345. — Windings of an 8 H. P. Arniatuie. 

A— 125 volts. B— 250 volts. C— 500 volts. 

per coil corresponding to 125, 250, and 500 volts. The speed 
and field strength are the same for each armature. In B and 
C two coils are shown per division, but they are connected in 
series as in case A. In a series closed circuit ring winding the 
same method will apply as given above. The end of the first 
coil is connected to the beginning of the second, and the 
junction, to commutator bar No. 2, and so on, until the end- 
ing of the last coil is connected to the beginning of the first 
coil and to bar No. 1. This 
method is outlined in the multi- 
polar ring armature in Fig. 359. 

336. Armature Core Loss — 
Hysteresis. — The iron core of an 
armature rotating in a two-pole 
field will be subjected to two 
opposite magnetic inductions in 
each revolution. For example, consider the polarity of the 
core at one instant during its revolution, Fig, 346 ; the left- 
hand side of the ring has a S-pole induced in it by the N-pole 
of the field magnet, while the right-hand side of the ring 
possesses an induced N-pole from the S-pole of the field 
magnet at the. same instant. At one-half revolution of the 
ring from this point that part which previously possessed in- 
duced N -polarity is now inductively magnetised with a 
S-pole, and the other half, with a N-pole. The ring is thus 




Fig. 346.- 



-Armature Core Loss- 
Hysteresis. 



362 



PRACTICAL ELECTRICITY. 




subjected to two opposite magnetisations in each revolution. 
Suppose the speed to be 2000 revolutions per minute, then 

there will be 4000 reversals of 
magnetisation per minute in 
the core. Heat is developed 
as a result of the hysteresis 
(page 308, Exp. 82). A por- 
tion of the energy required to 
drive the armature is thus ex- 
pended in heating the core and 
does not appear as useful elec- 
trical work. The heat so gen- 
erated also heats the copper 
wires wound upon the arma- 
ture core, increasing their resis- 
tance and the C 2 R loss, so that 
still more energy is wasted 
which does not appear as use- 
ful energy. This is called 
hysteresis loss in a dynamo. 
337. Armature Reactions. 
The current flowing from an armature circulates through its 
internal windings, and produces magnetic poles in the arma- 
ture core which react upon the magnetic field and distort it. 
Suppose current to be 
flowing in the direc- 
tion indicated, from 
the armature windings 
depicted in Fig. 347, 
a N and a S-pole are 
produced at diametri- 
cally opposite points, 
where the current en- 
ters and leaves the 
armature by the 
brushes, just as in the 
case of the plain iron 
ring C, of Fig. 178. 
Now when this arma- 



Fig. 347. — Magnetic Field Produced 

by Current Circulating Through 

the Armature. 




Sr^tfSS 



Fig. 348.— Eeaction of the Armature Field 
Upon That of the Field Magnets. 



ture is placed in its field and current flows from it, Fig. 348, 
its poles induce two poles in each of the field cores by mag- 
netic induction, with the polarities as indicated. 



ARMATURES. 



363 



One induced pole in each field core tends to strengthen the 
number of lines of force threading from the field to the arma- 
ture core, while the other induced pole tends to neutralize 
the field magnetism or to produce neutral points in the field at 
the opposite ends of a diameter. This will be more clearly 
understood from Fig. 349, which rep- 
resents the resultant distorted mag- 
netic field produced by the cross-mag- 
netising effect of the armature upon 
the field. The neutral points near 
two of the pole tips and the points 
where the lines are crowded under the 
other two pole tips are shown by the 
aid of iron filings. In the armature 
core, N and S represent the poles in- 
duced by the field magnets, while the 
poles in the core due to the armature 
current are represented by s and n. 

The position of maximum induction then is not along the 
horizontal line, as considered in the ideal dynamo 9 { \ 319, 
but along a line inclined at an angle to it, the angle increasing 
as the current from the armature increases. As a result of 




Fig. 349.— Distortion of 
the Magnetic Field Due to 
the Cross-Magnetising Ef- 
fect of the Armature Cur- 
rent. 



this field distortion the position of 




Fig. 350. — Neutral Points Produced by the 
Armature Reaction. 



minimum inductive 
action in the arma- 
ture coils will not 
be along the vertical 
line A B, Fig. 350, 
but along a line 
somewhat in ad- 
vance of it, in the 
direction of the ar- 
mature rotation, as 
the line CD which 
passes through both 
neutral points in 
the field and is 
known as the neu- 
tral line, or plane. 



Commutation of an armature coil must therefore take place 
as the coil passes the neutral line. The brushes should be 
set at diametrically opposite points (in a bipolar dynamo) 
and then shifted to a position corresponding with the neutral 



364 



PRACTICAL ELECTRICITY. 



line. The angle of advance of the neutral line from the 
vertical position will depend upon the current flowing from 
the armature (the held distortion increasing with the current) 
being shifted forward for an increase, and backward for a 
decrease in the armature current. The brushes must there- 
fore be shifted forward in the direction of rotation for an 
increase of current from the machine and backward, for a 
decrease. When the brushes are not set to correspond with 
the neutral point, sparking at the brushes will result. 

338. The Act of Commutation of an Armature Coil — 
Sparking at the Brushes. — The act of commutation of an arm- 
ature coil, that is, the 
"fr***w e moment it is passing 

from under the in- 
fluence of one pole to 
come under that of 
the other, is illustrated 
in Fig. 351. For an 
instant, each coil is 
completely short-cir- 
cuited by the toe of 
the brush, and any 
induced E. M. F. in 
the coil will cause a 
current to flow through 
it. As the coil moves 
away from the brush 
this circuit is broken and a bright spark appears at the point 
where the commutator bar leaves the brush, due to the self- 
induction of the coil produced by this current. Each coil is 
thus short-circuited as it passes underneath each brush, so 
that the sparking may become continuous when the dynamo 
is running. If the E. M. F. induced in an armature coil of 
.01 ohm resistance is only .1 volt at the neutral point, by 

F 1 

Ohm's Law the current for the instant will be ~ =-^r = 10 

amperes.* 

If the brushes are not exactly at the neutral point, the 
coils are then short-circuited before they reach the neutral 




Fig. 351. 



-The Act of Commutation of an 
Armature Coil. 

At the instant shown coil B is short-circuited by 
the brush. 



* Suppose that the brush in Fig. 351 had been made of copper instead of carbon, as is 
generally used, its resistance would have been less and a greater current would have 
circulated around the short-circuited coil, increasing the self-induction and probably 
melting a piece of the brush by the heat of the arc. 



ARMATURES. 



365 




Fig. 352. — Brushes Set Diametrically 

Opposite on the Commutator of 

a Bipolar Dynamo. 



point, and the E. M. F. in them is higher, causing a greater 
current to rise for the instant, which is noticed by an in- 
crease in sparking at the brushes. To find the neutral, or 
non-sparking point of a dynamo, when it is running, the brushes 
are rocked backward or forward until the sparking practically 
disappears, or until a point is 
found where it becomes a 
minimum. The tendency of 
a dynamo to spark can be 
entirely eliminated if, in 
construction, the armature 
is divided up into many 
coils. Each coil will then 
have only a few number of 
turns, which will keep the 
self-induction down, when, 
the induced E. M. F. will be 
very small, as a small coil 
can more nearly occupy the 
neutral point. The modern dynamo has been so perfected 
that the sparking has been entirely eliminated. Many 
dynamos, however, do spark at the brushes, but the fault 
lies in the manner of adjusting the brushes, etc., rather than 

in the machine itself. Some 
of the causes of sparking are 
given in ^| 340. 

339. Position of the 
Brushes. — The brushes must 
be first set on the commutator 
at the opposite ends of the 
diameter, in bipolar dynamos, 
or diametrically opposite. This 
is usually done by counting 
the number of bars in the com- 
mutator and then properly 
dividing them. Suppose that 
a commutator has 20 bars, the 
toe of the brush should then 
between bars 1 and 20, and 
in Fig. 352. In multipolar 




353. — Armature Winding. 



line 
as 



be set to the insulation 

between bars 10 and 11 

dynamos there are usually as many sets of brushes as pole 

pieces, so that the whole number of commutator bars is 



366 



PRACTICAL ELECTRICITY. 



divided into four equal parts for a 4-pole machine, and so on. 
Suppose a commutator of a 4-pole dynamo to consist of 144 
segments, then the toes of the brushes would be set to the 
insulation line between 144 and 1 ; 36 and 37 ; 72 and 73, 
and 108 and 109. To facilitate the construction and 
manipulation of the brushes in bipolar dynamos, the arma- 
ture coils are so connected that the brushes can be set at the 
ends of a horizontal diameter, and still be in connection 
with the armature coil as it is passing through the neutral 
point. This is accomplished by connecting the armature on the 
quarter, as it is termed. In Fig. 353 the terminals of coil 1 
are not connected to the commutator bar immediately below 
it, but carried around to a distance of one-quarter the whole 

number of bars and 
connected to bar 3. It 
will thus be seen that 
while coil 1 is in the 
vertical position, its 
terminals are at the 
end of a horizontal 
diameter, at which 
point the brushes 
should be located. In 
Fig. 354 is shown the 
relative position of the 
brushes of a 2-pole 
dynamo ; 1st, running- 
full load; 2d, half 




Fig. 354.— Shifting the Position of the Brushes 
3— No load. 2— Half load. 1— Full load. 



load; 3d, no load. 

The brushes are there- 
fore gradually advanced from position 3 to position 1 as 
the dynamo is loaded, and likewise rocked backward from 
1 to 3 as the load is diminished. The shaft which holds 
the brushes is attached to a cradle or arm, which can be 
moved to properly shift the brushes; hence the name 
" rocker arm." In some makes of dynamos the brushes, after 
being rocked to the neutral point, need not be again adjusted 
for any change in load. The neutral point in these ma- 
chines is made practically constant by designing the armature 
so that the armature poles will be saturated on light load. 
The neutral line will then be practically constant, instead of 
advancing with the increase in load. On account of the very 



ARMATURES. 367 

high potential used in arc light dynamos a small amount of 
sparking at the brushes is permissible. 

340. Causes of Sparking — 

1. Brushes are not set at the neutral point. They should 
be rocked till this position is found. 

2. Brushes are not properly spaced with reference to the 
commutator bars. They should be accurately and equally 
spaced by counting the bars between them. 

3. Brushes are not set with sufficient pressure against the 
commutator. 

4. Brushes are not set to obtain the full area of contact 
with the commutator. 

5. A high, low, or loose commutator bar causing poor con- 
tact with the brush. 

6. Loose connection between armature coil and commuta- 
tor bar. This will be noted by a peculiar blue snapping spark 
just as this particular bar passes under the brush. 

7. Commutator is worn in ridges, causing an uneven sur- 
face for brush contact. 

8. Armature section is short-circuited by a breakdown in 
the insulation, either in the coil or between commutator 
bars, causing a heating of the armature. If the machine 
can be stopped for a short time this coil should be discon- 
nected,, its ends taped, and a wire of the same size as that 
used in the armature used as a bridge to connect the com- 
mutator bars formerly connected to the detached coil. The 
continuity of the armature circuit will thus be maintained 
and the machine can be run till the coil can be rewound. 

9. Overload on the dynamo. This will be noted by the 
ammeter in the circuit, also by the sparking of the brushes 
and the increased temperature rise of the machine. 

10. Collection of dirt and grease on the commutator, which 
assists in preventing a good brush contact. 

11. Commutator bars are short-circuited by a collection of 
carbon or copper dust around them. The commutator 
should be kept clean, and generally requires no lubricant 
when carbon brushes are used. 

341. Capacity of a Dynamo. — With sufficient power 
applied to a dynamo it is possible to greatly increase the 
current which can be taken from it, but a limit is soon 
reached in one or more of three ways* 

*The student should read again fl 282 upon Lenz's Law for induced currents. 



368 PRACTICAL ELECTRICITY. 

First. By an excessive drop in the machine, due to an 
overload, which decreases the P. D at the brushes, when the 
lamps connected thereto will then receive insufficient current 
and burn dimly. The E. M. F. can be increased by increas- 
ing the speed, but from a mechanical standpoint there is a 
limit to the speed of rotation which cannot be exceeded, so 
that some of the load must be removed from the external 
circuit when this condition is attained. 

Second. By an excessive heating of the dynamo. As pre- 
viously stated the heat from the armature increases four-fold 
when the current from it is doubled, ^j 259. A machine 
might be operated with its copper conductors slightly below 
red-heat, but since this would destroy the insulation of the 
wires, internal closed circuits would then be formed, and the 
energy would not be conducted to the external circuit. It 
is not desirable to work a machine above the boiling point of 
water (212° F.) and generally the permissible rise is about 
70° above the surrounding air. In a hot engine room at a 
temperature of 100° F. then, the machine would be run at 
170° F. The temperature of a generator is determined by 
running it from 6 to 10 hours at full load, stopping it, and 
then placing thermometers against the hottest parts for a 
short time, as a half-hour, a piece of cotton-waste or other 
non-conductor of heat being laid over the thermometer. 

Third. By excessive sparking at the brushes of the gen- 
erator. This subject is treated in ^| 338. 

342. Commercial Rating of Dynamos. — Dynamos are 
rated in size, according to the number of kilowatts which 
they are capable of maintaining in the circuit external to 
their terminals within the limit of permissible heating. For 
example, a 60-K. W. 100- volt generator means that the ma- 
chine will deliver 60 K. W. to the circuit external to its 
terminals,* and that 100 volts P. D. will be maintained at 
this output across the terminals. The current, therefore, at 
full load will be, by Formula (63) 60000 -*- 100 = 600 am- 
peres. 

Owing to the electrical losses in the armature and fields 
the total K.W. generated is higher than the machine's rat- 

*The potential difference at the brushes and the terminals of shunt dynamos is prac- 
tically the same, but in a series or compound wound dynamo the potential at the 
brushes is higher than that at the terminals, on account of the C X R drop in the series 
field, flfl 351 and 353, The student should keep this point in mind when solving prob- 
lems. 



ARMATURES. 369 

ing. For example, the 60-kilowatt machine alluded to may 
develop 62.5 K.W., of which only 60 K.W. can be utilized 
in the external circuit. Compare with the power from cells, 

1|226. 

343. Losses in a Dynamo. — There are two classes of 
losses in a dynamo, 

(1.) Mechanical losses, 
(2. ) Electrical losses. 

(1) The mechanical losses include the friction between 
the rotating armature shaft and its journal bearings and the 
friction of the brushes upon the commutator. These friction 
losses are practically the same at all loads, and consume a 
certain percentage of the power supplied to the machine, 
which does not therefore appear as useful energy in the ex- 
ternal circuit. 

(2) The electrical losses include the C 2 R losses in the 
armature and fields, the losses due to eddy currents, ^[ 332 
and hysteresis, ^j 336. All the losses may be summed up 
then as due to, 

(a) Mechanical friction, 

(b) Electrical friction {resistance), 

(c) Magnetic friction (hysteresis). 

344. Efficiency of a Dynamo. — The meaning of the term 
efficiency is given in ^[ 227. There are two efficiencies of a 
dynamo, 

(a) Electrical efficiency, 

(b) Commercial efficiency. 

(a) Electrical Efficiency. — Electrical efficiency is the 
ratio of the electrical energy delivered to the external circuit 
to the total energy generated. The total electrical energy 
generated is equal to the energy delivered to the external 
circuit plus the C 2 R loss in the armature and the C 2 R loss in 
the fields or, 

W 

By Formula (84) Eff. = w ~ , 

when W = useful electrical energy, 
and w = energy lost in the machine. 

To Obtain the Electrical Efficiency of a Dynamo : 
Find the sum of the energy delivered, the loss in the armature 
24 



370 PRACTICAL ELECTRICITY. 

coils, and the loss in the field coils, and divide the energy delivered 
by this sum* 

Let W = useful or available energy ; 

w = loss in armature (C 2 r) ; 
w x = loss in field coils (C 2 r). 

W 
Then, Elec. Eff. = w , . . . .(102). 

W + w + Wj v J 

Prob. 122 : A dynamo delivers 40 K.W. to an external circuit and 
there is .6 K.W. lost in the field coils and 1 K.W. lost in the arma- 
ture. What is the electrical efficiency ? 

By Formula (102) Elec. Eff. ==__$?_ = 

J v J W+w + Wi 

^<^-M== 96 per cent. 

W = 40 K. W., w = 1 K. W., wj =.6 K.W. 

The electrical efficiency varies with the size of the dynamo ; 
a 1-K. W. dynamo may have as low an efficiency as 50 per 
cent ; a well designed 40- K. W. dynamo, 96 per cent, and 
generators of several thousand K.W. 98 per cent or more. 

(b) Commercial Efficiency. — Commercial efficiency is 
the practical rating of the machine and is the ratio of the 
energy delivered by it to the energy supplied to it, or, 

Commercial Efficiency = ^ t k * 

Commercial efficiency therefore includes the mechanical, 
electrical, and magnetic losses given in % 343. The com- 
mercial efficiency is always less than the electrical efficiency 
and varies with the size of the machine and the load it is 
supplying. For example, a 40-K.W. generator has an elec- 
trical efficiency of 96 per cent, while the commercial 
efficiency is, 

at J overload 89 per cent 

at full load 91 " 

at f load 89 

at | " 87 " 

at J " 84 " 

To Obtain the Commercial Efficiency : 
Divide the energy delivered by the dynamo by the sum of the 
mechanical, electrical, and magnetic losses. 

*The eddy currents and hysteresis losses are usually included in the mechanical 
losses since there is no direct method of measuring them. 






ARMATURES. 371 

Formula (84) applies to the commercial efficiency. 

Prob. 123 : It requires 44 K.W. (58 H. P. ) to drive the 40-K.W. dy- 
namo mentioned in Prob. 1?2. What is its commercial efficiency ? 

W 40 

By Formula (84) Com. Eff . = w , w = ^ =. 90 = 90 per cent. 

W= 40 K. W., W + w =44 K. W. 

QUESTIONS. 

1. What is meant by laminating an armature core ? Why is this 
necessary ? 

2. State three ways in which energy is unavoidably and uselessly 
expended in the internal actions of a dynamo. 

3. What are the neutral points of a dynamo ? 

4. Locate the neutral points in a bipolar dynamo when the arma- 
ture rotates against the hands of a clock. 

5. What is the hysteresis loss in a dynamo ? 

6. Sketch the position of a pair of brushes properly set upon a 
48-part commutator in a two-pole field. 

7. Why should a coil be commutated as it passes through the 
neutral point? 

8. Sketch the position of brushes properly set upon an 8-pole 
armature having 192 segments. 

9. Since a two-part commutator is so simple in construction, why 
are armature windings sub-divided into many coils, thus necessitating 
many commutator bar&? 

10. In some dynamos it is necessary to change the position of 
brushes for changes in the current flowing from the machine. Why 
is this? 

11. State some causes for sparking at the brushes of a dynamo. 

12. A piece of mica subjected to an insulation test is said to have 
broken down at 4500 volts. What is meant by this ? 

13. A ring armature contains a defective coil. How would you 
temporarily remedy the trouble so that the machine could be oper- 
ated? 

14. What is the difference between the electrical and commercial 
efficiency of a dynamo ? 

15. Explain what determines the capacity of a dynamo. 

16. The electrical efficiency of a 180-K. W. dynamo is 90 per cent. 
How much electrical energy is developed? Am. 200 K. W. 

17. If it requires 325 H. P. to drive the dynamo in question 16, 
what is its commercial efficiency ? Arts. 74 per cent. 



LESSON XXVIII. 



DIRECT CURRENT DYNAMOS. 




Fig. 355. — Bipolar Field Magnets. 



Bipolar Field Magnets — Multipolar Field Magnets — Multipolar Field 
Armature Circuit— Constant Current and Constant Potential 
Dynamos — Classification of Dynamos According to their Field 
Excitation— The Self-Exciting Principle of Direct Current Dyna- 
mos—Residual Volts — The Shunt Dynamo (Constant Potential) 
—Action of the Shunt Dynamo— Action of the Series Dynamo 
(Constant Current) — Compound Machines (Constant Potential) 
— Compound Wound Dynamos in Parallel-The Equalizer- 
Questions and Problems. 

345. Bipolar Field Magnets. — In the smaller size of 
dynamos employing a two-pole or bipolar field, the magnetic 
circuit has been designed 
in a variety of forms; the 
horseshoe type of field, as 
used in the Edison bipolar 
dynamo; the inverted horse- 
shoe type, Fig. 303, used in 
the Crocker- Wheeler and 
other makes, and the Manchester type of fields are very 
common forms. In the inverted horseshoe type the winding 

may be either upon 
the yoke as A, Fig. 
355, or upon each 
limb, as C, in the 
same figure.. The 
yoke thus serves as 
a bed- plate for the 
machine as well as 
to conduct the mag- 
netic lines of force. 
In the Manchester 
pattern there is a 
closed magnetic cir- 
cuit, B of Fig. 355, 
356. The 




Fig. 356.— Manchester Type of Field Frame. 

372 



also Fig 



DIRECT CURRENT DYNAMOS. 



373 




■Magnetic Circuit of Manchester 
Field Frame. 



yokes are cast iron, the lower one forming the bed-plate, 
and the magnet cores are of soft wrought iron. The magnet 
coils are connected so that the upper end of each limb tends 
to produce the same pole, a consequent pole is thus formed in 
each yoke, and the lines of force pass from yoke to yoke 
across the gap in which the armature is inserted. The direc- 
tion of the magnetic lines of force is depicted in Fig. 357. 

346. Multipolar Field Magnets. — The objection to a 
bipolar field is, that with a dynamo of large output the speed 

at which its armature 

would have to rotate to 
generate commercial 
voltages, would be 
prohibitive from a 
mechanical stand- 
point. By arranging a 
number oi electromag- 
nets with their poles 
extending inward from 
an iron ring, forming a multipolar field ring, the conductors 
upon the armature, revolving between them, cut the magnetic 
lines of force many more times in one revolution, so that, as 
the size of the machine increases the speed decreases. Slow 
speed is an advantage in any apparatus with moving parts, 
because there is less liability of derangement, less wear, and 
hence less need of frequent renewal of such parts. If a two- 
pole 45-K. W. dynamo is required to run at 
1000 revolutions per minute to generate an 
E. M. F. of 125 volts, a four-pole dynamo of 
equal output will run at only 500 revolu- 
tions ; one of eight poles, at only 250 rev- 
olutions per minute. Many four-pole field 
yokes are octagonal, but when more poles are 
required the ring form is used. The field 
magnet cores are generally cylindrical in 
form and constructed of cast " mild " steel (soft steel) con- 
taining a very small percentage of carbon, the magnetic 
quality of which is nearly equal to that of wrought iron. 
This is a much cheaper construction than where they are 
forged from wrought iron. The wrought iron or cast steel 
cores are cast-welded into the plain cast iron field ring, 
which, in the larger sizes, is generally divided into two parts, 




Fig. 358.— Multi 
polar Field Ring. 



374 



PRACTICAL ELECTRICITY. 



for convenience in handling. The coils are wound in the 
lathe, upon cast brass bobbins, which can be slipped directly- 
over the cores and fastened in place by bolts. Joints should 
be omitted in the magnetic field circuit for the reason given 
in ^[ 198, and all sharp corners, bolts, etc., should be rounded 
to prevent magnetic leakage. 

347. Multipolar Field Armature Circuits.— The circula- 
tion of current through the windings of a ring armature ro : 
tating in a four-pole field is shown in Fig. 359. The direction 
of rotation is clockwise, and the direction of current through 
the windings under any particular pole can be found by 
Fleming's Rule, ^| 278. The currents in the windings under 

the upper N and S -poles 
are opposed to each other 
and flow to the external 
circuit by the -f- brush 1 
and back to this half 
of the armature by — 
brushes 3 and 4. At the 
same instant the opposed 
currents in the lower 
windings flow to the ex- 
ternal circuit by -{- brush 

2 and return to the arma- 
ture through — brushes 

3 and 4. The armature 
is thus divided into four 
circuits and four brushes 
are required and must be 
placed between the poles 
so as to short-circuit the 
coils as they pass through 

the neutral space. In this form of winding there is no differ- 
ence of potential between the -f- brushes, so that they are con- 
nected in parallel, as are also the negative brushes, and then 
to the external circuit. In multipolar machines there are as 
many brushes as pole pieces,* and all the -\- brushes are gen- 
erally connected to one main generator cable, forming the -f- 
terminal of the machine, and likewise to the negative brushes. 

♦Since opposite commutator bars are of the same potential on this four-pole dynamo 
they may be joined by a cross-connecting wire and two brushes, as 2, and 4, dispensed 
with. This can only be done when there is an even number of coils. The armature 
is said to be " cross-connected." 







Fig. 359. — Direction of Current Through 

the Windings of a Ring Armature 

Rotating in a Four-Pole Field. 



DIRECT CURRENT DYNAMOS. 375 

348. Constant Current and Constant Potential Dyna- 
mos. — Alternators and direct current dynamos may be classi- 
fied according to their design as follows : 

(i.) Constant potential dynamos, 
(#.) Constant current dynamos. 

With constant potential dynamos the voltage is maintained 
constant across two or more parallel mains in which the cur- 
rent varies according to the resistance of the multiple circuit. 
Incandescent lighting, indoor arc lighting, motors and street 
railway systems are operated from multiple circuits connected 
to constant potential generators. In a constant current dynamo 
the current is maintained constant through an external series 
circuit connected to it, while the E. M. F. varies with each 
change in the resistance of the circuit. Street arc lamps are 
operated in series from constant current machines. The 
strength of the current is usually 9.6 amperes and the volt- 
age may vary from 45 to 8000 volts according to the number 
of lamps in circuit. The reason for operating these lamps in 
series is that they are generally distributed over a very large 
area, and a great economy in copper is effected by employing 
a small wire, generally about No. 6, for the series circuit and 
using a high voltage. The distribution of voltage through- 
out the circuit is much more uniform than would be possible 
with a multiple system, so that all the lamps regulate prop- 
erly. 

349. Classification of Dynamos According to Their 
Field Excitation. — The current for magnetising the field 
magnets of a dynamo may be supplied from a separate gene- 
rator or by the machine itself, when it would be styled either 
a separate or self-exciting dynamo. The methods of excita- 
tion are, of course, independent of the field construction and 
depend only upon the connections. A compound wound ma- 
chine is one in which the method of exciting the field mag- 
nets is a combination of two simple methods. Dynamos 
may be classified according to the methods used to excite the 
field magnets as follows : 

1. Simple Machines.— 

(a) Magneto Machines, Fig. 318. — The field magnets are 
permanent magnets and the machine used only for signalling 
or testing. It may give D. C. or A. C. currents. 



376 PRACTICAL ELECTRICITY. 

(b) Series Machines, A, Fig. 360 (Constant Current). — 
The field magnets are connected in series with the armature 
and wound with a few turns of heavy wire having a low 
resistance, so as not to oppose the main current flowing 
through them. 

(c) Shunt Machines, B, Fig. 360 (Constant Potential). — 
The field magnets are connected in parallel or shunt with the 
armature and are wound with many turns of small wire 
having a high resistance, compared with the armature, since 
only a small portion of the main current flows through 
them. 

(d) Separately Excited Machines, D, Fig. 360 (Con- 
stant Potential). — Current for the field magnets is supplied 
from a separate dynamo. 

2. Compound Machines. — 

(e) Series and Short Shunt Machines, F, Fig. 360 
(Constant Potential). — The field cores contain two independ- 
ent spools. One is wound with a few turns of heavy wire, 
forming the series coil and connected in series with the main 
circuit, the other, with a great many turns of smaller wire, 
forming the shunt coil and connected in shunt with the arma- 
ture. 

(f) Series and Long Shunt Machines, G, Fig. 360 (Con- 
stant Potential). — The same as (e) except that the shunt field 
shunts not only the armature but also the series field ; hence 
it is called a long shunt. 

3. Alternating Current Machines.— 

(g) Separately-excited Machines, D, Fig. 360 ( Constant 
Potential). — The field magnets are excited from an auxiliary 
dynamo called an exciter. Alternators require an exciter, 
since the alternating current cannot be employed to excite 
the fields. The exciter may be either a separate dynamo or 
an independent direct current winding upon the alternator 
shaft, Fig. 360, H. 

(h) Separate Coil, Self-contained Machines, C, Fig. 
360. — Separate coils wound on the armature core are con- 
nected to an independent commutator, which furnishes cur- 
rent for the field magnets. 

(j) Series and Separately-excited Machines, E, Fig. 
360. — Two independent field windings correspond to the series 



378 PRACTICAL ELECTRICITY. 

and shunt coils of F. The shunt coil is supplied from an 
exciter, while the main current, commuted, flows through 
the series field coils. This method is employed hi composite 
wound alternators, a portion of the main alternating current 
is commuted by a special device called a rectifier, located on 
the armature shaft. Its function is to change that portion 
of the alternating current intended for the series coils, into a 
direct current for producing the magnetisation. A self-con- 
tained separate coil alternator, composite w T ound, is depicted 
in H, Fig. 360. Details of the principal types are given in the 
paragraphs which follow. 

350. The Self-Exciting Principle of Direct Current 
Dynamos — Residual Volts. — In very early dynamos the 
field magnets were always separately excited by either a bat- 
tery or magneto machine. With the discovery of residual 
magnetism, ^[ 30, their self-exciting principle was recognized. 
If the soft iron or steel cores of a dynamo have once been 
magnetised they retain permanently a small amount of their 
magnetism. An armature revolving in even so weak a field 
as that due to residual magnetism will cut some lines of force, 
and as a result there is an E. M. F. maintained at the brushes 
without any excitation. This is often spoken of as the residual 
volts, and will be indicated upon a voltmeter connected to 
the brushes, when the field circuit is open, and the armature 
revolves at its proper speed. This E. M. F. may be from 2 
to 10 volts or more, depending upon the quality of the iron, the 
number of armature conductors, etc. If now the field cir- 
cuit be connected to the brushes, a current will flow through 
the field magnets due to the residual volts ; the number of 
lines of force of the field increases with this increase in field 
strength ; the induced volts also increase and cause addi- 
tional current to flow around the fields, resulting in a further 
increase of voltage at the brushes. This action continues 
until the maximum voltage of the machine is attained. The 
process has been termed " the building up of the fields," and 
may be noted either on a voltmeter, or by the gradual in- 
crease in the brilliancy of a lamp connected to the brushes, 
called a pilot lamp, when any direct current dynamo starts to 
generate. Ten to twenty seconds may be required from the 
time the field switch is closed until the armature generates its 
full voltage. A machine may refuse to build up, owing to 
the loss of its residual magnetism, when the cores should be 
remagnetised. 




c^ eo -*' ui «o . 



379 



380 



PRACTICAL ELECTRICITY. 



Prob. 124 : The resistance of the armature of a dynamo is .15 ohm 
and that of the field magnets, 100 ohms. With open fields the arma- 
ture generates 6 volts, due to the residual magnetism. What current 
will flow around the field to start the building-up process when the 
field circuit is closed-? 



By Formula (31) C 



6 



.059 ampere. 



R +r 100 + .15 

351. The Shunt Dynamo— Constant Potential— In a 
shunt dynamo, Fig. 362, the field coils are of compara- 
tively high resistance as compared with the armature ; for ex- 
ample, the multipolar field of a 125-volt, 11-K. W. dynamo 
has a resistance of about 40 ohms, and the armature resist- 
ance is only .095 ohm. The field 
ampere-turns of a shunt dynamo 
are the product of a very small 
current and a great many turns, 
so that little of the electric energy 
generated will be used for their 
excitation. The regulation of the 
voltage in the external circuit of 
a shunt machine is accomplished 
by varying the current through 
the field coils, by means of a 
resistance inserted in series with 
them, and called the field rheostat, 
Fig. 363. Decreasing the resist- 
ance in the field rheostat increases 
the current around the field coils, 
thereby increasing the ampere- 
turns, the number of lines of 
force cut by the armature, and the induced volts at the brush 
terminals. Inserting resistance in the field rheostat lowers 
the voltage at the brushes. 

The current flowing through the shunt field is equal to the 
potential difference at the brushes, divided by the resistance of the 
field plus the resistance in the field rheostat, Formula (28). 

The current flowing through the armature of a shunt dynamo 
is the sum of the currents in the field circuit and in the external 
circuit. The volts drop in the armature is equal to its resistance 
multiplied by the current flowing through it, Formula (29). 

The resistance of the armature is usually measured by the 
drop method, ^\ 241, and will be higher after the machine 




-Shunt Dynamo. 
The field magnets are connected across 
the brushes. B— Fig. 360. 



DIRECT CURRENT DYNAMOS. 



381 



has been carrying a load for some time, on account of the 
heating effect. 

352. Action of the Shunt Dynamo.— In starting a shunt 
dynamo, after proper speed is attained, the machine is brought 
up to the required voltage by the field rheostat, and then the 
main switch connecting it with the external circuit is closed. 
Suppose that the voltmeter indicates 112 volts potential differ- 
ence when the external circuit is open. The E. M. F. will 
be a little higher than this value and equal to 112 X C X r, 
where C equals the current through the fields and r equals the 
armature resistance. A voltmeter, therefore, placed across 
the brushes of any self-exciting dynamo indicates the poten- 
tial difference rather 

than the E. M. F. Re sistance b ox Tp- 1 : 1 I l- [ -J 

If the field rheostat fo I r-£-i voitmete. A 6 <S <S 6 6 
is adjusted for any 
particular voltage 
with the main cir- 
cuit open, say 112 
volts, and the 
switch is now closed 
so that more cur- 
rent flows from the 
armature, the volt- 
meter at once indi- 
cates a lower volt- 
age, say 108 volts. 
If the speed is the 
same as before, this 
loss is due to two 
causes : first, there is an increased drop in the armature due 
to the additional current flowing through it, which lowers the 
potential difference at the brushes ; second, the potential 
difference at the brushes being lowered, less current flows 
around the field, so that there are not quite so many lines of 
force cut as before. When the load is switched on to a shunt 
dynamo, the resistance in the field rheostat must therefore be 
diminished so that the voltage will be raised to its former value. 

Again, in the above case, if after the voltage is raised from 
108 to 112 volts the load be disconnected, the voltmeter will, 
indicate a higher voltage than 112 volts, say 116, and resist- 
ance must now be inserted in the field rheostat to lower the 




Fig. 363.— Regulating the E. M. F. at the Brushes 
of a Shunt dynamo by the Shunt Field Rheostat. 



382 



PRACTICAL ELECTRICITY. 



voltage. The potential difference at the brushes thus varies, 
in a shunt dynamo, with each change in load, increasing as 
the load decreases and decreasing as the load increases. If the 
current fluctuations are wide and quite frequent, as on trolley 
lines where the cars are started and stopped so often, an at- 
tendant would be constantly required to manipulate the 
rheostat, or some automatic device employed for this purpose, 
so that this machine is not suitable for such work. Shunt 
dynamos are adapted to cases where the load is constant 
when they will require very little attention after the proper 
regulation has been made ; they are classified as constant 
potential dynamos and may be connected in parallel when 




Fig. 364. — Two Shunt Dynamos Connected in Parallel. 

The voltage across the mains is equal to that of one machine, the maximum current 
on the mains, equal to the sum of that of the two machines. 

their voltages are equal. Shunt dynamos may be connected 
in parallel by connecting the positive and negative brushes 
as in Fig. 364. The voltage is the same as with one machine, 
but the current output will be the sum of the currents each 
machine can furnish separately. The voltage of the machine, 
to be paralled with other dynamos, should be adjusted equal 
to, or a little higher than their potential, when it can be con- 
nected to the common circuit. Such machines are practically 
self-adjusting to load conditions. If one machine runs a 
little faster than the rest it will do more work, and vice versa. 
Shunt dynamos will also operate in series, but if the ma- 
chines are of different sizes, the current in the external cir- 



DIRECT CURRENT DYNAMOS. 



383 



cuit is limited to the capacity of the smaller machine. 
The polarity of the brushes of a shunt dynamo may be 
changed by either reversing the field connections to the 
brushes, or by reversing the direction in which the armature 
rotates. In the latter case the brushes will also have to be 
changed to agree with the direction of rotation. 

Exp. 94 : The following test, No. 1, was made upon a 1.25-K. W. 
shunt wound dynamo and illustrates the falling of potential at the 
brushes as the load increases. The voltmeter was placed across the 
brushes, the ammeter, in series with some lamps joined in parallel, 
and the shunt field rheostat adjusted so that the E. M. F. was 110 
volts with no load. The rheostat was not adjusted thereafter during 
the test. 



Test No. 1. 



Test No. 2. 



Speed 


Volts at brushes 


Amperes 


Speed 


Volts at brushes 


1540 


110 


1 


2110 


100 


a 


106 


2 


2200 


104 


«< 


103 


3 


2290 


108 


<< 


100 


4 


2380 


112 


<< 


98 


5 


2470 


116 



Exp. 95 : The above test, No. 2, illustrates how the induced volts 
vary proportionally with the speed. The field magnets were sepa- 
rately excited so that the lines of force cut were the same at all 
speeds. 

Prob. 125 : A shunt dynamo, Fig. 365, maintains 110 volts across 
100 incandescent lamps joined in parallel, requiring 55 watts and 110 
volts each. The 

or 



lamps are lo- 
cated 100 feet 
from the dyna- 
mo and the re- 
sistance of the 
leads is .02 
ohm; 6.5 K. W. 




JLeads .oE.-ofvm. 

.03- ohm loo 

55"-Watf 
Lamps 




Fig. 365.— E. M. F. and P. D. of a Shunt Dynamo. 



are required to drive the dynamo. Resistance of armature .03, 
and fields 37 ohms. Find the following : 

(a) P. D. at brushes ; (b) total E. M. F. generated ; (c) watts lost 
in the armature ; (d) in the field ; (e) in the leads ; (f ) in the lamps, 
(g) What is the electrical efficiency? (h) What is the commercial 
efficiency ? 

W 55 1 

By Formula (63) C = ^, = ^ = -| X 100 = 50 amperes for lamps. 

(29) E = C X R = 50 X .02 = 1 volt drop in leads. 
110 + 1 = 111 volts P, P, at brushes (a), 



384 



PRACTICAL ELECTRICITY. 



(28)0 = ^ = ^ = 3 amperes through the fields. 

50 + 3 = 53 amperes through the armature. 
(29) E = C X R = 53 X .03 = 1.59 volts lost in arma- 
ture. 
1.59 + 111 = 112.59 volts total E. M. F. (b). 
(62) W = E X C = 1.59 X 53 = 84.27 watts lost arma- 
ture (c). 
Ill x 3= 333 watts lost in fields (d). 
1 X 50 = 50 watts lost in leads (e). 
110 X 50 = 5500 watts lost in lamps (f ). 
W 5500 + 50 



(102) Elec. Eff. 



.93 



W + w 



5550 + 84.27 



333 



(84) Com. Eff. = 



93 per cent (g). 

w-T^- = PS! = .85 = 85 percent (h). 
W -4- w 6o00 r v ' 



353. Action of the Series Dynamo (Constant Current). 
— In a series dynamo, Fig. 366, the field coils are in series 
with the armature, and have a low resistance, since the cur- 
rent from the armature flows 
through them to the external cir- 
cuit.* The field ampere-turns 
of a series dynamo, as distin- 
guished from the shunt machine, 
are the product of a much larger 
current and a less number of 
turns. With the armature running 
at a constant speed, the E. M. F. 
and current from a series dynamo 
will vary with every change in 
the resistance of the external cir- 
cuit, since each change of current 
alters the field magnetising cur- 
rent, and consequently, the E. 
M. F. induced in the armature. In 
practice the current from a series 
dynamo is required to be con- 
stant, irrespective of the resistance of the external circuit, 
while the voltage is altered to suit the conditions of the cir- 
cuit. It is thus a constant current dynamo. The regulation is 
accomplished by either of two general methods. In the first 

*For example, the field magnets of a 160-light Brush series arc dynamo have a resist- 
ance of 17.2 ohms and the armature for the combination given in % 331, has a resistance; 
of 18 ohms. The loss in the armature is thus nearly the same as in the field. 




Fig. 366.— Series Dynamo. 
The fields are in series with the arma- 
ture. A— Fig. 360. 



DIRECT CURRENT DYNAMOS. 



385 



method the armature used is of the open coil type, ^f 331, and 
the position of the brushes is automatically moved so as to be 
in connection with the armature coils while they are passing 
through any stage of induction, from the points of maximum 
induced E. M. F. to the minimum, or neutral points. Any 
change in the current strength tending to change the field 
magnetism is thus neutralized by a corresponding opposite 
change in the E. M. F. The automatic regulator is usually 
a solenoid and core attached to the brushes and actuated by 
the main current. This method is utilized in the Thomson- 
Houston arc light dynamo. In the second method an ad- 
justable rheostat is placed in shunt with the series field mag- 
nets, Figs. 366, 367, and the main current divides in propor- 
tion to the resistances of the two circuits. The arm of the 

rheostat is auto- 

,. -,, j , . Series Field 

arrangement actu- 
ated by the main 
current. If the re- 
sistance of the ex- 
ternal circuit is 
suddenly lowered, 
the increased cur- 
rent immediately 
actuates the sole- 
noid and rheostat 
arm in a direction 
to decrease its re- 
sistance, thereby shunting more current from the field circuit, 
and preventing the rise of E. M. F. When the external resist- 
ance is increased the resistance in the rheostat is automati- 
cally increased and more current flows around the field mag- 
nets, thus increasing the E. M. F. This second method is used 
in the Brush arc light generator. Obviously a series dynamo 
will not self-excite when the external circuit is open, and will 
not ." build up" when the external resistance is very high. 
This may be overcome by momentarily short-circuiting the 
machine while the external circuit is closed, when the E. M. F. 
will rise to a sufficient value to start the action. With a 
sensitive automatic regulator a series machine may be short- 




367. — Regulating the Voltage of a Series 
Dynamo by Shunting the Series Field. 



circuited without 
25 



injury, since the larger current which 



386 



PRACTICAL ELECTRICITY. 



would tend to flow, immediately actuates the automatic 
mechanism in such a manner as to decrease the E. M. F. 

354. Compound Machines (Constant Potential). — The 
compound wound dynamo is designed to automatically give 
a better regulation of voltage on constant potential cir- 
cuits than is possible with a shunt machine, and possesses the 
characteristics of both the series and shunt dynamos. The 
shunt field is the same as in the shunt dynamo, and inde- 
pendent series field spools are added, through which the main 
current flows. These are connected so as to increase the 
magnetism of each pole produced by the shunt winding, Fig. 
368. With no current in the external circuit the machine 
separately excites by its shunt field. When current flows 
to the external circuit the voltage at the brushes is not 
lowered, as in the shunt dynamo, since the series winding 

strengthens the field 
by the current flow- 
ing through it, and 
thus raises the volt- 
age in proportion 
to the increased 
current. By a 
proper selection of 
the number of turns 
in the series coils, 
the voltage is thus 
kept automatically 
constant for wide 
fluctuations in load 
without changing the shunt field rheostat. If a greater 
number of turns is used in the series coil than required 
for constant voltage at all loads, the voltage will rise as 
the load is increased, and thus make up for the loss on 
the transmission lines, so that a constant voltage will 
then be maintained at some distant point from the generator. 
The machine is then said to be over-compounded. This over- 
compounding is usually designed for a rise of voltage from 5 
to 10 per cent of that of the machine, from no load to full 
load. In design, the field coils are wound with a greater 
number of turns than actually required, and the machine is 
accurately compounded by a running load test after com- 
pletion. These adjustments are made by placing a German 




Fig. 368. — Compound Wound Dynamo. 
The series and shunt field act in unison. F — Fig. 



DIRECT CURRENT DYNAMOS. 



387 



silver shunt in parallel with the series field so that the main 
current divides between the two circuits, Z, Fig. 371 ; also 
19, of Fig. 361. The length of the shunt can then be regu- 
lated to send sufficient current around the series coils to pro- 
duce the desired compounding. In a short shunt compound 
wound generator the. shunt field is subjected to a higher 
voltage than in the long shunt connections. The E. M. F. 
applied to the shunt field in the latter case for any particular 
load, being equal to the E. M. F. at the brushes plus the drop 
on the series field, F and G of Fig. 360. Compound wound 
direct current dynamos are used in incandescent electric light- 




Fig. 369.— 100-K. W. 125- Volt Multipolar Compound Wound D. C. Dynamo 
Direct-connected to a Steam Engine. 

Output at brushes, 800 amperes at 125 volts. Speed, 270 revolutions. Poles, 6. Approxi- 
mate horse power required to drive generator, 150 H. P. Approximate weight : 
armature and commutator, 2,950 pounds; generator complete, 11.200 pounds. 

ing stations and in electric railway power stations where the 
load is very fluctuating. A short circuit on a compound wound 
dynamo overloads the machine, since the excessive current 
flowing through the series field tends to keep the voltage at 
its normal value. Unless the line is automatically opened 
under such a condition either by a fuse or circuit breaker, 
the machine and its driving engine will be damaged. To 
avoid heavy short circuits, which would damage such genera- 
tors as well as their engines, they are protected by automatic 
circuit breakers, Fig. 176. 



388 



PRACTICAL ELECTRICITY 



Exp. 96: The following test was made on the 1.25-K. W. dynamo, 
referred to in Exp. 94. The series field was short-circuited in the 
previous tests. Both fields are acting in the present case. The ma- 
chine was adjusted to 110 volts by the shunt field rheostat as before, 
and not changed during the test. It will be noted that the potential 
is constant whether 1 lamp or 5 lamps are in circuit. Compare with 
the shunt dynamo test in f 352. 

Compound-Wound Dynamo Test. 



Speed. 


Volts at 
Brushes 


Amperes. 


1540 
1540 
1540 
1540 
1540 


110 
110 
110 
110 
110 


1 
2 
3 
4 
5 



Prob. 126 : A compound wound dynamo supplies 100 amperes at 
112 volts to a group of lamps located 75 feet from the generator. Re- 
sistance of leads .02 ohm ; armature .01 ohm ; series coil .02 ohm ; 
shunt coil 40 ohms ; 14 K. W. are required to drive the machine, 
Fig. 370. Find the following : 

(a) P. D. at brushes ; (b) total E. M. F. generated ; (c) watts lost 
in the leads ; (d) in the series ; (e) in the shunt ; (f ) in the arma- 
ture ; (g) in the lamps, (h) What is the electrical efficiency ? (k) 
What is the commercial efficiency ? 



Series .OEOH-m 




Leads .o£ ohm 



(vm) 



he 

VoltS. 



OO Amperes 



7^ Feet- 



g 



Fig. 370.— E. M. F. and P. D. of a Compound Wound Dynamo. 



By Formula (29) E 
(29) E 

(28) C 



2 volts drop in leads. 

D. at terminals. 

2 volts drop on series 



z C X R = 100 X .02 = 
112 + 2 = 114 volts P. 
= G X R = 100 X .02 = 

field. 

114 -f 2 = 116 volts P. D. at brushes (a). 
116 volts across shunt field. 

= -j| =^ = 2.9 amperes through shunt field. 



100 + 2.9 = 102.9 amperes, 
through armature. 



total current 



DIRECT CURRENT DYNAMOS. 389 

(29) E = CXR= 102.9 X .01 == 1.029 volts drop in 
armature. 
E. M. F. — 112 volts (lamps) + 2 volts 
(leads) + 2 volts (series) + 1.029 volts 
(armature) = 117.029 volts (b). 
(68) W = C 2 R = 100 X 100 X .02 == 200 watts (c); 
= 100 X 100 X .02 = 200 watts (d); 
= 2.9 X 2.9 X 40 = 336.4 watts (e); 
= 102.9 X 102.9 X .01 = 105.884 watts 
(f). 
(62) W = E X C =114 X 100 == 11400 watts external 
circuit (g). 
117.029 X 102.9= 12042.28 watts generated. 

(102) Elec. Eff. = w+ ^ Wi = S = ■« 
= 94fo (h). 
(84) Com. Eff. = ^-. = noTo = ' 81 = «* «' 

355. Compound Wound Dynamos in Parallel — The 
Equalizer. — Compound wound dynamos are generally run 
in parallel, but more care must be exercised in connecting 
them in circuit than with the shunt machine. In order to 
connect several compound wound dynamos in parallel a 
special regulating device, called an equalizing bar must be 
used. The function of this equalizer is to enable each ma- 
chine to take its share of the load and to make the load on 
the machines so paralleled, independent of slight changes in 
speed. The equalizing bar, Fig. 371, connects the brush of 
one dynamo, to which the series field is attached, to the cor- 
responding brush of another dynamo. Both brushes, so 
connected, are of the same polarity and also of the same po- 
tential when the machines run at the same voltage. The 
action is as follows : suppose the compound wound dynamo 
No. 1, Fig. 371, is carrying a load and it is desired to par- 
allel machine No. 2 with it ; the latter is brought up to speed 
and its voltage regulated by the shunt field rheostat till a 
voltmeter indicates that it is equal to that of No. 1. Though 
the terminals of the loaded and free machines are now equal 
in voltage the voltage at the brushes of the loaded machine 
will be higher than that of the other, by an amount equal to 
the drop on the series field of No. 1. There is thus a dif- 
ference of potential between the two ends of the equalizing 
bar, and wmen this switch (E) is closed, some current flows 



390 



PRACTICAL ELECTRICITY. 



through the equalizer and around the series field of machine 
No. 2 to the external circuit. The line switch S 2 is now 
closed and the free machine takes some portion of the load 
and is further regulated by its shunt field rheostat. When 
complete equalization of load occurs there will be no current 
in the equalizer. If the speed of either machine falls, 
thereby lowering its voltage, current from the other machine 
will flow through the equalizer and strengthen its series 
field, thus increasing the voltage. There is thus sometimes 
no current in an equalizer while at other times it may be flow- 
ing in either one direction or the other. To reduce the C 2 R 
loss, the equalizer should be as short as possible and as large 




$m (teller Rheostat 



Fig. 371. — Two Compound Wound Dynamos Connected in Parallel. 



as the main dynamo cables. A triple pole switch is gener- 
ally used for coupling a compound dynamo with others, the 
middle blade of which is slightly longer than the other two, 
and is connected to the equalizer. When the switch is closed 
the equalizer is thus connected first, and the main terminals 
a little later. In shutting down a dynamo in parallel with 
others the main line terminals are first disconnected and then 
the equalizer, which is performed in one operation with the 
triple pole switch alluded to above. The voltage should 
then be lowered by inserting all the resistance of the shunt 
field rheostat in circuit, when this field circuit switch may be 
opened, and then the speed reduced. Any number of com- 
pound dynamos may be operated in parallel. If the ma- 
chines are of different capacities they may also be run in 
parallel, provided that the voltages are the same, and resist- 
ances of the series fields made inversely proportional to the 



DIRECT CURRENT DYNAMOS. 391 

current capacities of the several machines to be connected. 
Each machine will then take load in proportion to its ca- 
pacity. The series fields can be adjusted by adding several 
turns of extra wire to this circuit, as required. See Plate II. 

QUESTIONS. 

1. Why are large dynamos constructed with multipolar rather 
than bipolar fields ? 

2. Sketch a ring armature located in a six-pole multipolar field, 
indicating the polarity of brushes and fields, and direction of current 
from the armature. 

3. What is the distinction between constant current and constant 
potential dynamos? 

4. What is a compound-wound dynamo ? 

5. Since the field magnets of a self-exciting dynamo are not sup- 
plied with current from any external source, how is it possible for 
the machine to generate ? 

6. A 110- volt incandescent lamp is connected to the terminals of a 
series machine running at its proper speed and capable of generating 
4000 volts, yet the lamp fails to light, Why is this ? 

7. The main switch of a shunt dynamo is closed and then the ma- 
chine started up, but it refuses to " build up." Why is this ? 

8. A large number of lights are suddenly switched off from a 
circuit connected to a shunt dynamo. What two actions will imme- 
diately occur at the generator and how will vou counteract them ? 

9. What are " residual volts " ? 

10. Give two reasons for the fall of potential at the brushes of a 
shunt dynamo when the current from it is increased. 

11. What is the advantage of a compound-w r ound generator over a 
shunt type of machine? 

12. What is the difference in the method of regulating the field 
magnetising force of a series and shunt machine ? 

13. A generator is compounded for 10 per cent of its rated voltage. 
What is meant by this and how is it accomplished,? 

14. What is meant by an over-compounded generator? 

15. Since an alternating current is not suitable for magnetising its 
field magnets, how can an alternator be self-exciting ? 

16. What is an exciter, and for what is it used ? 

17. What will be the effect of joining two shunt dynamos in series 
if one machine is rated at 45 K. W. and the other at 100 K. W ? Both 
machines have the same E. M. F. 

18. What is an equalizing bar, and for what purpose is it used ? 

19. How would you proceed to parallel a compound wound D. C. 
machine, wdrich is " shut down," with two others carrying loads ? 

20. How 7 would you disconnect and shut down one of the machines 
in question 19 ? 

21. Make diagramatic sketches of all the different methods of field 
excitation with which you are familiar, 



392 PRACTICAL ELECTRICITY. 



PROBLEMS. 

1. A series dynamo has a resistance of .03 ohm ; the field coils, .01 
ohm ; the machine is connected to an arc lamp requiring 14 amperes 
and having a resistance of 4 ohms ; the resistance of the lead wires 
is .4 ohm. The machine requires 1£ H. P. to drive it. Find the fol- 
lowing : (a) Total E. M. F. generated. (6) P. D. at the brushes, (c) 
Electrical efficiency, (b) Commercial efficiency. Ans. (a) 62.16 volts ; 
(6) 61.74 volts ; (c) 99 %; (d) 77 %. 

2. A shunt dynamo is connected to 150 lamps, connected in parallel, 
each having a resistance of 60 ohms (hot), and requiring .85 ampere. 
The resistance of the armature is .02 ohm ; field magnets, 22 ohms ; 
leads neglected, (a) Find the E. M. F. (6) What is the P. D. ? Ans. 
(a) 53.596 volts ; (6) 51 volts. 

3. A compound wound short shunt dynamo is connected to 700 in- 
candescent lamps in parallel, each having a resistance of 220 ohms (hot) 
and requiring 110 volts. Eesistance of leads, .02 ohm ; shunt field, 40 
ohms ; series field, .015 ohm ; armature, .025 ohm. It requires 70 
H. P. to drive the machine. Find the following : (a) E. M. F. gen- 
erated, (b) P. D. at brushes, (c) Drop on series field, (d) Watts 
lost in shunt field, (e) Watts lost on the line. (/) Electrical effi- 
ciency, (g) Commercial efficiencv. (h) Make complete sketch. Ans. 
{a) 131.076 volts ; (6) 122.25 volts; (c) 5.25 volts ; (d) 373.565 watts; 
{e) 2450 watts ; (/) 88 %;(g)7&%. 

4. The series coil of a short shunt compound dynamo, connected to 
450 .6-ampere 100-volt lamps in parallel, is .009 ohm. The resistance 
of the leads is .2 ohm. (a) What is the P. D. at the brushes ? (6) At 
the machine terminals? Ans. (a) 156.43 volts ; (6) 154 volts. 



LESSON XXIX. 

DIRECT CURRENT MOTORS. 

Comparison Between a Dynamo and a Motor— Principles of the 
Motor — Direction of Rotation of Series and Shunt Motors— Posi- 
tion of the Brushes on a Motor — Counter Electromotive Force of 
a Motor — Normal Speed of a Motor — Mechanical Work Performed 
by a Motor-Torque— Output and Rating of Motors— Moto Speed 
and Torque— Methods of Motor Speed Regulation— Speed Regu- 
lation of Series Motors (Second Method) — Series Motors for 
Railway Work — Operating Motors— Efficiency of a Motor — Elec- 
tric Traction — Questions and Problems. 

356. Comparison Between a Dynamo and a Motor. — 

A dynamo is a machine for generating electrical energy by 
moving conductors in a magnetic field, the force necessary to 
maintain the motion being supplied by a steam engine or 
other source of power. An electric motor is just the reverse 
of a dynamo, and is a machine for converting electrical 
power supplied to it into mechanical power at the motor 
pulley. When the field magnets of a dynamo, as Fig. 303, 
are excited and a current is passed through its armature by 
means of the brushes, the armature will revolve in the mag- 
netic field . The rotation is due to the electrodynamic action 
between the magnetic field of the current-carrying wires upon 
the armature, and that produced by the field magnets. An 
electric motor, for direct currents, is constructed in the same 
manner as a dynamo. Any machine that can be used as a 
dynamo will, when supplied with electrical power, run as an 
electric motor, and conversely, an electric motor, when driven 
by mechanical power, will supply electrical energy to the 
circuit connected to it. Thus, a dynamo and motor are con- 
vertible machines, and the previous lessons upon the con- 
struction of dynamos will apply equally as well to the electric 
motor. Motors are classified in the same manner as dynamos 
and may be, 

(a) Series wound, 

(b) Shunt wound, 

(c) Covipound woimd, 

393 



394 



PRACTICAL ELECTRICITY. 



The fields may be either bipolar or multipolar, and since 
the number of poles determines the number of neutral points, 
there must be as many brushes as poles, except when th'e 
commutator is cross-connected, page 333. 

357. Principles of the Motor.— The principles involved 
in the rotation of the armature conductors, when placed in a 
magnetic field, are fully discussed under the subject of elec- 
trodynamics, Lesson XXIII. It was there experimentally 
shown how a single loop, placed in a magnetic field, could be 
made to rotate, by commutating the current through it at the 
proper instant in a revolution, U 275, and how the turning- 




Fig. 372.— Parts of a 20-H. P. Direct Current Slow Speed Motor. 

K. W., 15. Volts, 250. Amperes, 60. Speed, 600 revolutions per minute. Average net 
weight, 2460 pounds. Diameter of pulley, 14 inches ; face, 8 inches. 

effort was increased by increasing the number of loops or 
coils and arranging them at different angles with reference to 
the field.* When the loops are angularly disposed around an 
iron core, as in a Gramme or drum ring armature, and then 
placed in a powerful magnetic field and a current passed 
through them, each loop tends to move to the position in 
which it encloses the greatest number of the lines of the 
field. The direction in which each loop will move will be such 
that its lines of force will be in the same direction as the 

* The student is advised to agaiq read If 275, 



DIRECT CURRENT MOTORS. 395 

lines of force of the field ; the force with which it will move, 
or the turning effort or torque, ^[ 362, will depend upon the 
strength of current flowing through it (that is, the strength 
of current driving the motor), the size of the loop, and the 
density of the lines of force through it. When the loop 
arrives at the position where it accommodates the greatest 
number of the lines of force through it in the same direction 
as its own lines, the force, or turning effort, stops. If moved 
past this position the electrodynamic force is reversed and 
now tends to turn the coil back to the position of maximum 
lines of force through it. To obtain continuous rotation, the 
current through each loop must be reversed at the instant 
that the turning effort ceases. These reversals are automat- 
ically performed by the commutator. The drum or Gramme 
ring armatures fulfill these conditions, their commutators re- 
versing the current through the coils at the proper instant, 
when the brushes are correctly set and adjusted. 

In a dynamo the direction of current in the armature is 
such as to oppose the motion producing it, Lenz's Law ; the 
reaction increased as the current from it increased, thereby 
requiring additional power to drive it as the load increased. 
The reaction of the current in the armature of a dynamo is 
thus opposed to the direction of rotation of the armature. 

In a motor, the reaction of the magnetic field of the arma- 
ture conductors upon the magnetic field surrounding them is 
such as to move the armature wires across the field in the 
same direction as the armature rotates, and it is this force 
which is used to perform mechanical work at the motor 
pulley. The greater the load applied to the pulley of a motor 
the greater will be this force or turning effort (torque), and 
consequently the greater the current taken by the motor 
armature from the supply mains. 

358. Direction of Rotation of Series and Shunt 
Motors. — The direction of rotation of a motor, or that in 
which any dynamo will rotate when used as a motor, can be 
found by the left-hand rule, page 278, when the polarity of 
the field magnets and the direction of current through the 
armature have been ascertained. Place the left hand, as 
shown in Fig. 243, so that the fingers correspond with the 
polarity and direction of current in the single armature coil 
motor, Fig. 373, and it is found that the loop will rotate in 
the direction of the hands of a clock , The direction of rota- 



396 



PRACTICAL ELECTRICITY. 




l -=|iIHit- j 



Fig. 373. — Single Loop Armature 
Driven as a Motor. 

The dotted arrows indicate the direc- 
tion of counter E. M. F. 



Hon of a motor can be changed by reversing the current 
either through the armature or through the fields, but not 
through both. If both are changed, the motor will run in 
the same direction as before. See page 279. 

A series dynamo when supplied with current becomes a 
series motor, Fig. 366, and will run in the opposite direction 
to its motion as a generator. Reversing the direction of cur- 
rent at its terminals will not 
change the direction of rotation, 
since the current still flows 
through the armature in the same 
direction as through the field, 
Fig. 366. Reverse either the 
armature or field connections to 
change the direction of motion. 

A shunt dynamo runs in the 
same direction when used as a 
shunt motor, Fig. 362, as when 
used as a generator. This will 
be seen from Fig. 362 ; if the cur- 
rent, from an external source, 
enters by the lower brush it will flow up through the 
armature in the same direction as when it is used as a dyamo, 
but the current through the fields will be reversed from the 
direction indicated in the figure, since the fields are in par- 
allel with the brushes. 

Exp. 97 : Connect the student's experimental dynamo, Fig. 309, as 
a shunt motor, Fig. 362 ; adjust the brushes so as to make contact 
with the collector rings ; place the armature coil with its plane hori- 
zontal and pass a current through the motor. The coil is urged around 
until its plane becomes vertical, when rotation ceases, according to 
the principle outlined in ^ 357. Incline the coil at any angle to the 
vertical position, and upon closing the circuit it rotates to the vertical 
position and stops. 

Exp. 98 : Now adjust the brushes upon the two-part commutator 
and repeat Exp. 97. The coil rotates continuously in one direction 
at several hundred revolutions per minute. The direction of current 
is reversed by the commutator at each half revolution. 

Exp. 99 : Find the polarity of the field magnets with a compass, 
also the polarity of the supply line, and note whether the direction 
of rotation is according to the left-hand rule, page 278. 

Exp. 100 : Reverse the current at the motor terminals and the 
direction of rotation is the same as before. Why? Now reverse the 
direction of rotation, ^ 267. 

Exp. 101 ; Connect the motor armature in series with the two field 



DIRECT CURRENT MOTORS. 



397 



coils in parallel, so that the poles have the proper polarity, N and S. 
It is now a series motor, (a) Apply the left-hand rule, page 278, for 
the direction of rotation of the armature, (b) Reverse the direction 
of rotation, as in If 267. 

359. Position of the Brushes on a Motor. — The reaction 
of the armature current upon the field of a motor distorts it 
just as in a generator, ^[ 337. The lines of force are, how- 
ever, now crowded together under the opposite pole tips to 
those illustrated in Fig. 349. The neutral line, or plane will, 
therefore, advance backward against the direction of rotation 
of the motor, and it is at this position commutation in a mo- 
tor should take place. The brushes are set in the same man- 
ner as given for a dynamo in % 339, but are rocked backward 
against the direction of rotation till the neutral point or non- 
sparking position is found. The angle of advance against the 
direction of rotation will increase as the current taken by the 



\lfA]l07.3S Volts 




H. P. driving dynamo = 32.7. i Watts intake by motors, 20868.84 watts. 

Efficiency of dynamo, 90^. Efficiency of motor, 8(K. 

Useful watts generated= 21967.2 (29.4 H. P.) I Useful power developed by motor, 22.3 H.P. 
General efficiency of the entire transmission system, 68^. 
Fig. 374. — Electrical Power Transmission. 

motor increases, or as the work it is required to perform in- 
creases, and decrease as the load is removed. The conditions 
and remedies for the sparking at the brushes of a motor are 
the same as those given in \\ 340. 

360. Counter Electromotive Force of a Motor.— The 
armature wires of a motor, rotating in its own magnetic field, 
cut the lines of force just as if it were being driven as a dyna- 
mo, and consequently there is an induced E. M. F. in them. 
By applying the right and left-hand rules to the single coil in 
Fig. 373, it will be seen that if it is rotated clockwise, the di- 



398 PRACTICAL ELECTRICITY. 

rection of the induced E. M. F. will tend to send a current 
around the coil from A to B, to C, to D, while when supplied 
with current as a motor, to rotate in the same direction, the 
applied pressure will oppose the induced pressure and cause 
a current to flow from D to C, to B, to A. This induced mo- 
tor pressure is called the Counter Electromotive Force (ab- 
breviated C. E. M. F.) and is always in such a direction as 
to oppose the direction of the pressure applied to the motor \ 
terminals, or to that of the supply mains. The dotted arrows, 
in Fig. 373, indicate the direction of the counter E. M. F. and 
the solid arrows, that of the applied E. M. F. as found by 
the right and left-hand rules. This counter E. M. F. is a very 
important property possessed by the motor, as will be shown 
later on. A motor, without load, will run at such a speed 
that its counter E. M. F. will very nearly equal the applied 
pressure. 

The counter E. M. F. of a motor running at any speed 
will be the same as when it is run as a generator at this 
speed, provided the field strength is the same in both cases, 
hence to find the counter E. M. F. of a motor at any speed : 
run it as a generator at this speed and measure the induced 
E. M. F. by a voltmeter. The counter E. M. F. may also be 
observed by connecting a lamp across the terminals of a shunt 
motor, running without much load, and opening the main 
supply circuit when the lamp will still be illuminated and 
gradually become dim as the speed of the motor decreases. 
A voltmeter connected across the motor terminals will also 
indicate, by the direction of the needle's deflection, that the 
counter E. M. F. is opposed to that of the line E. M. F. when 
the supply switch is opened. 

To Find the Current Flowing Through the Armature 
of a Motor : 

Subtract the counter E. M. F. from the applied E. M. F. and 
divide this result by the armature resistance. Ohm's Law for a 
motor, then, is as follows : 

Let E = E. M. F. applied at motor brushes ; 
g = counter E. M. F. developed by motor ; 
= current through motor armature ; 
r = internal resistance of motor armature. 

Then, C = ^=^ (103). 

Also by transposition, § = E — (C X r) (104). 



DIRECT CURRENT MOTORS. 399 

The counter E. M. F. can never equal the E. M. F. , but is al- 
ways less by an amount equal to the drop in the motor arma- 
ture (C X r). The difference between a dynamo and motor is 
as follows : 



Dynamo. 

The Mechanical Driving 
Force is Equal and Opposite 
to the Counter Electrodyna- 
mic Force. 

The E. M. F. is Greater 
Than the Pressure at the Ter- 
minals. 



Motor. 

The Electrodynamic Driv- 
ing Force is Equal and Oppo- 
site to the Mechanical Force 
op the Driven Machinery. 

The Counter E. M. F. is 
Less Than the Pressure at the 
Terminals. 



To Find the Counter E. M. F. of a Motor : 

Multiply the resistance of the armature by the current flowing 

through it and subtract this product from the E. M. F. applied to 

the motor brushes, Formula (10 4.). 

The counter E. M. F. of a motor depends upon the same 

factors as those governing the induced E. M. F. in a dynamo, 

and is directly proportional to, 

(a) The number of lines of force cut, 

(b) The number of conductors upon the armature, 

(c) The speed at which the lines of force are cut. 

To Find the Mechanical Power Developed by a Motor : 
Multiply the counter E. M. F. by the current through the arma- 
ture. 

W = S X C (105). 

The mechanical power developed includes that required 
for mechanical friction losses and the power which is ex- 
pended in eddy currents and hysteresis. 

Prob. 127 : A small motor is connected to a 110-volt circuit ; the 
counter E. M. F. at a particular speed is 100 volts ; the resistance of 
the armature is 2 ohms. What current is being supplied to the 
motor ? 

By Formula (103) C = E ~^ = 110 ~ 100 = 5 amperes. 

E = 110 volts, g = 100 volts, r = 2 ohms. 

Prob. 128 : The armature resistance of a shunt wound motor is .5 
ohm, and at a certain load 10 amperes flow through it ; the drop across 
the motor brushes is 110 volts. What is the counter E. M. F. ? 

ByFormula (104) g = E-(CX r) = 110— (10 X .5) =105 volte. 
E = 110 volts, C = 10 amperes, r = .5 ohm. 



400 



PRACTICAL ELECTRICITY. 



Prob. 129 : What current would the motor referred to in Prob. 127 
receive if it had no counter E. M. F.? 



By Formula (28) C 



110 

2 : 



55 amperes. 



E = 110 volts, R = 2 ohms. 

Prob. 130 : (a) What power is developed by the motor in Prob. 
127? (b) What power is supplied to the motor? (c) What is the 
commercial efficiency of the motor (friction losses being neglected) ? 

By Formula (105) W = g X C = 100 X 5 = 500 watts (a). 



By Formula (62) W = E X O=110 X 5 = 550 watts (b). 

,90-90% (c] 



W 500 

By Formula (84) Com. Eff. = ^~^ = gg 



There is no counter E. M. F. induced in a motor armature 
until it begins to revolve, so that the current flowing through 
it, when stationary, is equal to E -*- R, as in Prob. 129. When 

the armature begins to rotate, 
the current through it gradu- 
ally diminishes, since the 
counter E. M. F. rises with the 
speed. It requires more energy 
to start a motor than to main- 
tain it at any particular speed, 
^f 210, so that the counter 
E. M. F. automatically acts 
like resistance in a circuit, and 
decreases the current as the 
speed increases. 

The great advantage, then, 
of counter E. M. F, in a motor 
is that it regulates the current 
without absorbing the elec- 
trical energy, as in a rheostat, 
where the extra energy is dissipated as heat; motors can 
thus be run very economically. The automatic regulation of 
the current, as the motor attains its normal speed, is shoAvn 
in the following experiment : 

Exp. 102 : An ammeter is connected in series with the armature of 
a small motor and the current noted for several speeds read from an 
automatic speed indicator (tachometer) as follows : 




Fig. 375. — Motor Windings Protected 
by Cast Iron Housing. 



DIRECT CURRENT MOTORS. 



401 



Table XXII.-Motor Test. 



Speed— Revolutions 
per minute. 


Amperes. 


Speed — Revolutions 
per minute. 


Amperes. 




500 

1000 


20.0 
16.2 
12 2 


1600 
1800 
1950 


7.8 
6.1 
5.1 



At the maximum speed the motor in the above test receives 5.1 
amperes, or about one-fourth of the current which would flow through 
it at rest. If some machinery be now connected to the motor pulley 
by a belt, the motor will slow down somewhat, thus decreasing the 
counter E. M. F. and permitting more current to flow through the 
armature to perform the extra work. When the load is removed 
the motor increases in speed, thus increasing the counter E. M. F. 
and decreasing the current taken from the line. There is thus 
a continual automatic adjustment between the current supplied 
to a motor and the work it has to perform, or the electrical power taken 
from the supply mains by a motor is directly proportional to the mechanical 
power it is required to develop at its pulley. This drop in speed of a 
shunt motor, running fully loaded, may be 5 per cent less than the 
speed the motor attains when running free. 

361. Normal Speed of a Motor. — Suppose a shunt 
dynamo maintains a P. D. of 110 volts at its brushes when 
driven at a speed of 1800 revolutions, and that it is now run 
as a motor, and 110 volts maintained across the brushes. 
The field strength will be the same as when it was run as a 
generator, but the speed at which the motor will run will 
be less than 1800 revolutions, because at this speed the 
counter E. M. F. would be equal to the applied E. M. F., 
and this would be impossible, since the motor would then 
receive no current from the line. The counter E. M. F. 
equals the applied E. M. F. minus the drop in the arma- 
ture, Formula (104). 

Suppose the above motor attains a speed of 1600 revolu- 
tions. When run as a generator, the induced E. M. F. per 

revolution will be ^— ^ = .061 volt per revolution. At 1600 

revolutions the counter E. M. F. equals 1600 X .061 = 97.6 
volts. The drop in the armature is thus the difference be- 
tween the applied pressure and the counter E. M. F., or 
110 — 97.6=12.4 volts. If the resistance of the motor 
armature is .2 ohm, then the current the armature receives 
when running at 1600 revolutions, is 12.4 -*- .2 = 62 am- 
peres, Formula (28). The watts lost in the motor armature 
26 



402 PRACTICAL ELECTRICITY. 

will be, Formula (62), 12.4 X 62 = 768.8 watts; the watts 
applied to the armature, Formula (62), 110 X 62 = 6820 
watts (9.1 H. P.), and the useful power* developed by 
the motor will be equal to the product of the counter E. M. 
F. and the armature current, Formula (105), or 97.6 X 62 = 
6051.2 watts (8.1 H. P.). Suppose the motor fields receive 3 
amperes, then the energy from the line expended in the fields 
= 3 X 110 = 330 watts ; or total energy supplied to the motor 
= 6820 + 330 = 7150 watts (9.5 H. P.) intake and motor 
output = 6051.2 watts (8.1 H. P.). The commercial efficiency 
of the motor is from Formula (84) and *j[ 369. 

The speed which any motor attains is such that the sum of the 
counter E. M. F. developed and the drop in the armature is ex- 
actly equal to the applied E. M. F. This is expressed by the 
following formula derived by transposition from Formula 
(104): 

Counter E. M. F. + (C X r) = applied E. M. F., 

or S+ (C Xr)=E (106). 

The drop in the armature of a motor is a small percentage 
of the applied pressure, about 2 per cent of the terminal 
pressure in a 500-K. W. motor and about 5 per cent in a 
1-K. W. motor, so that the counter E. M. F. nearly equals 
the applied E. M. F. Since the power driving a motor equals 
the applied pressure times the current, most of which is use- 
fully expended in mechanical output, the counter E. M. F. 
is an essential and valuable feature of the motor, rather than 
a detriment to its operation. 

362. Mechanical Work Performed by a Motor- 
Torque. — The mechanical work performed by a motor de- 
pends upon two factors, the speed and the torque, and is 
equal to the product of these factors, ^| 213. The term 
" torque " is applied to the twisting force which is produced in 
the armature when a current is sent through it, and repre- 
sents the effort made to cause rotation. This effort is made 
up of two components ; first, the pull, measured in pounds, 
and second, the length of arm at which this pull acts ; that 
is, the distance measured in feet from the centre of the 

* Neglecting friction losses, etc. 




DIRECT CURRENT MOTORS. 403 

shaft to the point at which the pull is applied. For exam- 
ple, suppose that the turning effort of the motor pulley, P, 
one foot in radius, Fig. 376, is just balanced when a weight 
of 1000 pounds is supported from the pulley ; the torque, 
which is measured in foot-pounds, is in this case, 1 foot X 
1000 lbs. = 1000 ft. lbs. No work is per- 
formed by the motor, since the pulley does 
not revolve (W =FXS,U 213). Suppose 
now that the armature pulley has a radius 
of 2 feet, and that the electrodynamic force 
is sufficient to lift a weight of 1000 pounds, 
Fig. 376 ; the motor torque is then 2 feet X 
1000 lbs. = 2000 ft, lbs.* At each revolu- 
tion of the pulley the weight will be lifted a 
distance equal to its circumference,! or 
2 tt X r=2 X 3.1416 X 2 = 12.5664 feet; 
the amount of work performed per revolu- 
tion = 12.566 ft. X 1000 lbs. == 12,566 ft. 
lbs. If the motor makes 500 revolutions 
per minute the total work performed = Flg - pu 6 iiT^ otor 
12566 X 500 = 6,283,000 ft. lbs., and since 
one mechanical horse power r= 33,000 ft. lbs. of work per- 
formed per minute, page 211, the rate of working in the 
above motor is 6,283,000 - 33,000 = 190.3 horse power. 

363. Output and Rating of Motors. — The capacity of 
a motor to perform useful work is limited by the same condi- 
tions as those governing the capacity of a generator, ^J 341. 
Motors are commercially rated according to the amount of 
power they will maintain at full load, at their pulleys, within 
the limit of permissible heating. For example, a 10-K. W. 
110-volt motor will, when supplied with 110 volts at its 
terminals, develop 10 K. W. or 13.4 horse poAver at the 
pulley. A dynamo will have less capacity when driven as 
a motor than when driven as a generator, since in the latter 
case the driving engine furnishes the additional power to 
overcome the friction and internal losses, while a motor must 
develop this extra power. For example, suppose it requires 
17 K. W. from an engine to drive a dynamo with 15 K. W. 

* With a pulley 1 foot in radius, the corresponding torque would lift 2000 pounds. 

t The Greek letter TV (pi) represents the relation between the diameter of a circle and its 
circumference, and is equal to 3.1416. Circumference of a circle = 7T X d, where d = the 
diameter. 



404 PRACTICAL ELECTRICITY. 

output, wound to deliver 100 amperes to the external circuit 
at full load, and this machine is to be used as a motor. The 
permissible intake, within the heating limit, will be 15 
K. W. at 100 amperes, and since 2 K. W. were previously 
required for friction losses, eddy currents, etc., only about 13 
K. W. output will be available at the motor pulley. A motor 
will thus be somewhat larger than a generator of the same 
capacity. 

364. Motor Speed and Torque. — There are three dif- 
ferent classes of work to be performed by motors, requiring 
as many different conditions of motor speed and torque, as 
well as a particular type of motor for the work to be 
performed. 

First. When a motor is required to drive a crane, a hoist, 
or an elevator, it must run with constant torque at a variable 
speed, since the load is constant and is to be moved at vary- 
ing rates of speed. 

Second. A motor used to drive a line shaft in a machine 
shop must run at constant speed, regardless of the number 
of machines in operation, or the work being performed by 
them, which illustrates the case of variable torque arid a con- 
stant speed. 

Third. Both of the above conditions are encountered in 
street railway work where the motor is required to develop a 
variable torque and variable speed ; for example, in starting 
a car the torque required is a maximum and the speed a 
minimum ; when the car gains some headway the torque 
diminishes and the speed increases. 

Thus, according to the character of the work to be performed, 
motors must develop either, 

(a) Constant torque at variable speed, 
(6) Variable torque at constant speed, 
(c) Variable torque at variable speed. 

A series wound motor operated from constant potential mains 
is generally used for cases (a) and (c), while a shunt motor 
operated from a constant potential circuit fulfils the condi- 
tions required in case (b). Ordinarily, direct current motors 
are built for 110, 220 or 500-volt constant potential circuits; 
the advantage of the higher potential motor being, that for 
a given amount of power to be developed, a smaller size lead 
wire is required ; for example, the size of wire required to 



DIRECT CURRENT MOTORS. 405 

transmit 10 K. W. at 500 volts must be sufficient to carry 20 
amperes, Formula (63) ; at 200 volts, 50 amperes ; and at 
100 volts, 100 amperes. The greater the number of field 
poles the lower will be the motor speed to develop any given 
power. 

365. Methods of Motor Speed Regulation.— The follow- 
ing two methods are usually employed for regulating the 
speed of motors connected to constant potential circuits : 

(i) By inserting resistance in the armature circuit of a shunt 
ivound motor. 

(#) By varying the field strength of series motors by switching 
sections of the field coils in or out of circuit. 

First method. — This method is depicted in the upper half 
of Fig. 378. When the switch, A, is closed the motor fields 
are first excited and by moving the arm, S, of the rheostat to 
point 1, the armature circuit is completed with the extra re- 
sistance in series with it. Suppose a shunt motor to be ope- 
rated from a 100- volt circuit, requiring 50 amperes to pro- 
duce the required torque for a particular load, and that the 
resistance of the armature and extra resistance in series with 
it, 1 to 5, Fig. 378, is 2 ohms. By Formula (29) the drop 
on this resistance with a current of 50 amperes through it is 
100 volts, so that the motor armature is not required to de- 
velop any counter E. M. F., or it remains at rest, supporting 
the weight from its pulley but not moving it. Reduce the 
resistance in the armature circuit to, say 1.5 ohms, by mov- 
ing S to point 3 ; the motor armature now turns and runs at 
such a speed that the counter E. M. F. will be equal to the 
value of drop on the resistance so cut out (or 50 X .5 = 25 
volts) and the weight is lifted at a proportionate speed. With 
the armature at rest 5 K. W. (100 X 50) were uselessly ex- 
pended in heating the resistance ; in the second instance a 
portion of this energy appeared as useful work. Continue to 
decrease the resistance in the armature circuit by moving arm 
S to the right, and the speed increases and a greater portion 
of the energy is available for useful work. This is not an 
economical method of regulating the speed of a motor, since 
the energy taken from the line (5 K. W.) is the same whether 
the motor be running at a very slow speed or at a high 
one. The rheostat used for series regulation of this charac- 
ter must be of such a capacity as to carry nearly the entire 
intake of the motor without injurious heating. 



406 



PRACTICAL ELECTRICITY. 



366. Speed Regulation of Series Motors — Second 
Method. — The method of regulating the speed of a series 
wound motor, by increasing or decreasing its field strength 
by varying the turns around the field, is illustrated in Fig. 

377. The current .through 
the motor armature will flow 
through all the field wind- 
ings when the position of 
the switch arm, S, is on 



point 1, so that the field will 
then have its maximum 
strength and will be de- 
creased as the arm is moved 
to point 2, 3, etc. Increasing 
the field strength of a motor 
decreases its speed, while de- 
creasing the field strength in- 
creases the speed* This is 
shown by the following ex- 
ample. Suppose a street car to be running on a level road at 
such a speed that the motor develops a counter E. M. F. of 
400 volts, while the applied E. M. F. is 500 volts ; assume 
the resistance of the armature to be 1 ohm. The motor 
current will be : 




Fig. 



377.— Speed Regulation of a 
Series Motor. 



By Formula (103) C 



E — g_500 — 400 



= 100 amperes. 



r 1 

The power developed by the motor will be, 

By Formula (105) W= g X C = 400 X 100 = 40000 watts (53.6 
H. P.). 

Suppose it is desired to run the car more slowly. Increase 
the field strength, say 10 per cent, by moving switch, S, so as 
to insert more turns in the field circuit. The counter E. M. 
F. at the same speed as before would be 10 per cent higher, 
or 440 volts, and the current received by the motor, 

E — g_500 — 440 



By Formula (103) C 



= 60 amperes, 



r 1 

or the power now developed, 
By Formula (105) g X C = 440 X 60 = 26400 watts (35.3 H. P. ). 



*In a dynamo increasing the field strength increases the E. M. F., while decreasing it 
decreases the E. M. F. - 



DIRECT CURRENT MOTORS. 407 

Since it required 53.5 horse power to maintain the first 
speed the car must now run more slowly when the motor 
develops only 35.3 H. P. ' 

Under the conditions of maximum field strength of a motor, 
as with switch S on point 1, the torque will be greatest for any 
given current strength, and the counter E. M. F. also greatest 
at any given speed. The current through the armature of 
the motor, to perform any given work, will thus be a mini- 
mum, as well as the speed at which the motor has to run, in 
order to develop sufficient counter E. M. F. to permit this 
current to flow. If" the field strength could be increased in- 
definitely it would then be possible to make the motor de- 
velop a very high counter E. M. F at a very low speed. With 
very light loads, then, to be moved at a slow rate of speed, the 
motor would take current from the line in proportion to the 
load. Suppose the load is to be moved more rapidly ; de- 
creasing the field magnetising force permits the motor to 
attain a higher speed to generate its necessary counter E. M. 
F. at the reduced field strength, with correspondingly more 
current taken from the line, since the rate of working at the 
higher speed is increased. Regulation of speed by varying 
the field strength is limited in range of action, since the field 
saturation point is soon reached ; on the other hand, with too 
low a field strength the armature reaction upon the field pro- 
duces excessive field distortion, sparking, etc. 

The speed of a series motor may be nearly doubled by this 
method of regulation, that is, if the lowest permissible speed 
is 250 revolutions it may be increased to 500 revolutions. In 
practice this regulation is effected by commutating the field 
coils, from series to parallel ; for example, suppose 50 am- 
peres to flow through two sections of a field coil containing 
100 turns each, the total turns are therefore 200 and the mag- 
netising force, Formula (54), 50 X200 = 10000 A. T. With 
the two coils in parallel and 50 amperes through the circuit 
the total magnetising force is now only 5000 A. T., so that the 
field strength is diminished. By this method the resistance 
of the motor circuit is also lessened, so that, to some extent, 
the method includes the rheostat control described in % 365, 
but is far more economical for the reasons given above. A 
rheostat inserted in the field circuit of a shunt motor will 
regulate the speed, within limits, in the same manner. 

367. Series Motors for Railway Work. — Series motors 



408 PRACTICAL ELECTRICITY. 

are used for railway work, because they best fulfill all the re- 
quirements, such as powerful torque at starting, variable 
speed and economical speed regulation for varying loads. 
When two motors are used their armatures and field coils are 
connected in series with each other and an extra resistance, 
which prevents too great a rush of current from the mains 
before the car starts. As the car gains headway a barrel 
cylinder switch termed a series-parallel controller * gradually 
cuts the extra resistance out of circuit and commutates the 
field windings from series connection to parallel, and, finally, 
connects each motor directly across the mains, or between the 
overhead trolley line and the track, which is used as the ground 
return ; one terminal of the station generator being con- 
nected to the trolley line and the other to the track. The 
fields of series railway motors are designed so as to become 
saturated with less than the total current required by the 
motor at full load. When the resistance of the field circuit 
is diminished a higher P. D. is applied at the motor brushes, 
causing a higher speed to be maintained by reason of the 
additional armature current. This current also flows around 
the field, but being saturated there is no tendency to decrease 
the speed, as would be the case if the field were below satur- 
ation point. In this manner different E. M. F. 's may be 
applied to the armature without affecting the field strength. 
Complete connections for two standard series motors, as 
used on the ordinary trolley car, are given in Plate II. 

368. Operating Motors. — The resistance of the armature 
of motors is very low ; for example, the armature of a 220- 
volt 10-K. W. shunt motor has a resistance of about .2 ohm. 
If this motor were directly connected to the supply mains, as 
by closing the switch A, Fig. 378, a much greater current 
than that required for full load would flow through it before 
any counter E. M. F. could be developed, resulting in damage 
to the windings ; the low resistance would practically short- 
circuit the mains, causing an excessive drop of voltage. See 
Prob. 129. For this reason a rheostat, called a starting 
box, Fig. 378, is always inserted in the armature circuit of a 
shunt motor to prevent this extra rush of current before the 
motor attains its speed. The value of this extra resistance 
should be such that, when added to the armature resistance, 

* Plate II illustrates a general electric type K series-parallel controller, and gives a 
diagram of the several combinations. 



DIRECT CURRENT MOTORS. 



409 



it would permit only the 
full load current taken 
by the motor to flow 
from the mains. As the 
motor attains some speed, 
and counter E. M. F., 
this resistance is gradu- 
ally cut out by moving 
arm, S, from post 1, ta 2, 
to 3, etc., until at point 5 
the line is directly con- 
nected across the motor. 
For example, to start the 
shunt motor close switch, 
A, when the motor fields 
will be excited ; move 
the arm, S, of the start- 
ing box to point 1, when 
the armature circuit will 
be completed in series 
with the extra resistance ; 
cut out the extra resist- 
ance as the motor attains 
speed by gradually mov- 
ing S to point 5. To 
stop the motor, open the 
main switch, A, and then 
place the arm of the 
starting box on the off 
position, so that the 
motor will be ready for 
re-starting. 

In an automatic motor 
starting box, such as that 
depicted in Fig. 123, the 
arm, S, carries a small 
piece of iron, P, Fig. 378, 
and turns against the 
action of a spring ; an 
electromagnet, M, in 
series with the shunt 
field is mounted on the 



fwm 



»h > 

Shunt Field 




MOTOR 



Starting 
"Rheostat 




DYNAMO~~7/ 



Shu-at "Field- 
■Rheostat 



Shunt Field 

KSiSmSL 



^-M 



Fig. 378.— Connections of a Shunt Motor 
to a Dynamo Circuit. 



410 PRACTICAL ELECTRICITY. 

box, and when arm, S, rests on point 5 it is held there by the 
electromagnet against the action of the spring. The advantage 
of this arrangement is, that if for any reason the main power 
supply circuit should be interrupted, the starting box arm 
will automatically open the circuit and shut the motor down, 
instead of permitting the motor armature to cause' a short- 
circuit across the mains when the power is again turned on. 

Shunt motors should be started with the driven load dis- 
connected, it being switched on to the motor when the maxi- 
mum speed is attained. In starting a shunt motor always be 
sure that the fields are first excited (test their attractive power 
with a penknife), since without the field excitation the arm- 
ature could not generate a counter E. M. F., but would take 
an excessive current from the line. 

The resistance and the self-induction of the armature and 
fields of a series motor tend to check the sudden rush of cur- 
rent through it, so that in some cases this motor might be 
directly connected to the mains without injurious effects. 
Usually, however, some extra resistance is connected in the 
motor circuit, and gradually cut out as before. 

369. Efficiency of a Motor. — The commercial efficiency 
of a motor, as in the case of the dynamo, ^f 344, is the ratio 
of the output to the intake. The energy furnished to the 
motor is readily measured, and from this must be subtracted 
the losses in the motor to obtain the available energy. These 
losses are divided into two classes : the C 2 R losses in the arm- 
ature and fields, and the mechanical losses, which include 
friction, eddy currents and hysteresis. 

Prob. 131 : The pressure applied to a motor having a resistance of 
2 ohms is 110 volts. What power is developed by the motor when 
the counter E. M. F. is (a) 80 volts? (b) 55 volts? (c) 40 volts? 

By Formula (103) C = ?-=-? = no ~ 80 = 15 amperes. 

By Formula (105) W= § X C = 80 X 15 = 1200 watts (a) ; 

also 110 2 ~ 55 = 27.5 amperes, 

and 27.5 X 55 = 1512.5 watts (b) ; 

also ^ — = s- = 35 amperes, 

and 35 X 40 = 1400 watts (c). 



DIRECT CURRENT MOTORS. 411 

From this problem it will be noted that the power devel- 
oped by a motor increases as the counter E. M. F. decreases, 
until the counter E. M. F. equals one-half the applied E. M. 
F., after which point the motor develops less power as the 
counter E. M. F. decreases. The maximum work is done 
when the counter E. M. F. is just equal to one-half the ap- 
plied E. M. F. 

370. Electric Traction. — The chief factor in stationary 
motors is the work the motor can perform without becoming 
too warm or decreasing too much in speed, while in street 
car motors the most prominent factor is the torque, or the 
tractive force, the motor is capable of developing at different 
speeds with different loads. 

The tractive force is the force exerted by the motor on the car in 
the direction of its motion. 

On a level road the tractive force of a motor varies with a 
number of conditions, such as road bed, track, lubrication of 
journals, weight, etc. 

The tractive force varies directly as the weight of the car and 
the passengers carried. For average conditions about 25 
pounds tractive force (torque) are required for each ton pro- 
pelled by the motor on a level road, with a speed of from 
6 to 10 miles per hour. For example, to propel a car weigh- 
ing 6 tons, with passengers aboard weighing 3 tons, will re- 
quire a tractive effort on a level of 9 X 25 or 225 pounds. 

To Find the Watts Required to Propel a Street Car 
on a Level Road at a Certain Speed : 

Multiply the tractive force by the speed in feet per minute to 
obtain the foot-pounds of work performed per minute, and divide 
by 33, 000 to obtain the horse power ; multiply the H. P. by 746 
to obtain the watts output of the motor, and divide this product 
by the efficiency of the motor to obtain the watts required by the 
motor from the line, Formula {107). 

Let W = watts required by the motor on level road ; 
F = tractive force = 25 lbs. per ton ; 
% M — efficiency of the motor ; 

T = weight of the car and passengers, in tons ; 
S = speed of car, in feet, per minute. 

Then, W = ^yL£-® X 746 

3 ( g°Q? (107.) 

% M 



412 PRACTICAL ELECTRICITY. 

Prob. 132 : A street car weighs 7 tons, and the passengers aboard, 
3 tons ; the tractive force is 25 pounds per ton ; efficiency of motor, 
75%. How many watts are supplied to the motors when the car is 
propelled at a speed of 10 miles an hour on a level road? 

Total weight = 7 + 3 = 10 tons X 25 = 250 pounds tractive force. 

Feet traveled per minute = 10 * 5280 = 880. 

oO 

Foot-pounds of work per minute = 880 X 250 = 220000. 
Horse power developed by motor = ?n? = 6 - 6 - 
Watts developed by motors = 6.6 X 746 = 4923.6. 
Watts delivered to motors = ^|p = 6564.8. 

Or by Formula (107 ) W = T 33^0* S X 746 



M 



10 X 25 X 880 x 746 



33000 

= 6564.8 watts. 



.75 

When the car ascends a grade a certain amount of addi- 
tional energy is required to propel it, and this is represented by 
the amount of energy required to raise the car through the 
distance it travels vertically. 

To Find the Additional Power Required to Enable a 
Car to Climb a Grade : 

Multiply the per cent of the grade * by the speed of the car in 
feet per minute, to obtain the vertical distance traveled per minute ; 
multiply this product by the weight of the car and the passengers, 
expressed in pounds, to obtain the total foot-pounds of work per- 
formed ; divide this product by 33,000 to obtain the horse power, 
and multiply the, quotient by 7^6 to obtain the ivatts output of the 
motor ; divide this residt by the efficiency of the motor to obtain 
the watts taken from the line, Formula (108). 

Let %G = the per cent of grade ; 

Wj = additional watts required to ascend the grade ; 
T x = weight of car and passengers, in pounds. 

Then, W 1= = %G 4nn XTl X 746 

33000 (108). 

* A 10 per cent grade means a vertical rise of 10 feet in every hundred feet traveled ; 
a 7 per cent grade, 7 feet, etc. 



DIRECT CURRENT MOTORS. 413 

To Find the Total Watts Required For a Car to As- 
cend a Grade : 

Add the ivatts required for a level road to the additional watts 
required for the grade, Formula (109). 

Total watts required = W 4- W t (109). 

Prob. 133 : How many watts must be supplied to the motors in 
Prob. 132, in order that the car will ascend a 10 % grade? 

Vertical rise in feet per minute = 880 X .10 = 88. 
Total weight of car, in pounds = 10 X 2000 = 20000. 
Foot-pounds of work per minute = 20000 X 88 = 1,760,000. 

Ho^powe r = ™=53.3 

Watts output of motors = 53.3 X 746 =39761. 

Watts required by motors = — ==- =53015, or by Formula (108) 



w _ % G X S X T, 7 , fi .10 X 880 X 200 00 7 , fi 
1_ 33000 X /4b ' 33000 X ' ^ 



53015. 



% M .75 

By Formula (109) total watts required = W+ Wj = 6564.8 + 53015 
=59579 watts or 59.5 K. W. 

QUESTIONS. 

1. How does a motor differ from a dynamo ? 

2. What is the difference between a shunt and series motor? 

3. A series dynamo rotates clockwise. What will be the direction 
of rotation when it is used as a motor ? 

4. A shunt dynamo runs in a counter clockwise direction. How 
will it run when driven as a motor ? 

5. What is necessary in order to properly run the shunt dynamo 
in question 4 as a shunt motor and in a clockwise direction? 

6. Since the counter E. M. F. of a motor permits less current to 
flow through it than if it did not exist, and the turning effort of a 
motor depends on the current through the armature, of what advan- 
tage then is the counter E. M. F. ? 

7. State two methods by which you can prove a motor to possess 
counter E. M. F. 

8. How would you measure the counter E. M. F. of a motor? 

9. Upon what factors does the counter E. M. F. depend ? 

10. A shunt motor is called a constant speed motor ; how is it possi- 
ble then for the motor to take current from the line in proportion to 
the power it develops, since if it always runs at constant speed 
the counter E. M. F. would be constant, and therefore the current 
constant ? 

11. Why is it impossible for the counter E. M. F. of a motor to 
attain a value equal to the applied E. M. F. ? 

12. A 15-K. W. shunt motor is to be used as a dynamo. Will its 
output be more or less than 15 K. W. ? Why? 



414 PRACTICAL ELECTRICITY. 

13. What factors determine the mechanical work which can be 
performed by a motor ? 

14. What is meant by motor torque ? 

15. What is the difference between motor speed and motor torque ? 

16. State the conditions of torque and speed that motors are re- 
quired to develop in commercial work, and the kind of motor adapted 
to each case. 

17. Explain two methods of motor speed regulation, stating the 
advantage or disadvantage of each method. Illustrate your answer 
by sketches. 

PROBLEMS. 

1. A shunt motor having an armature resistance of 2 ohms and a 
field resistance of 125 ohms is connected to a 250-volt main and de- 
velops a counter E. M. F. of 220 volts. What current is taken from 
the line? Ans. 17 amperes. 

2. What mechanical power is developed by the motor in problem 
1 ? Ans. 4.4 H. P. 

3. If there are 500 watts lost in mechanical friction, hysteresis 
and eddy currents in the motor in problem 1, what useful power 
can the motor develop ? Ans. 3.7 H. P. 

4. What is the commercial efficiency of the motor mentioned in 
the above problem ? Ans. 65 % . 

5. Fifty amperes flow through a motor armature havng a resist- 
ance of 3 ohms when it is connected to a 250 volt supply circuit. 
What counter E. M. F. is developed ? Ans. 100 volts. 

6. What mechanical power is developed by the motor armature in 
problem 5? Ans. 6.7 H. P. 

7. A shunt motor runs at 1400 revolutions ; when connected to a 
220-volt circuit and driven as a dynamo it generates 220 volts P. D. 
at a speed of 1600 revolutions. What is the counter E. M. F. when 
the machine is used as a motor ? Ans. 182 volts. 

8. The resistance of the armature in problem 7 is 2 ohms. What 
current flows through it when it is run as a motor ? Ans. 19 amperes. 

9. The fields of the motor in problems 7 and 8 receive 5 amperes ; 
if 458 watts are required for mechanical losses what is the commercial 
efficiency? Ans. 56%. 

10c A motor pulley has a diameter of 18 inches and runs at 400 
revolutions per minute when exerting a pull of 2000 pounds, (a) 
What is the motor torque ? (b) What horse power is being developed 
by the motor? Ans. (a) 1500 ft. lbs. ; (6) 114.2 H. P. 

11. The counter E. M. F. of a motor is 230 volts ; the current 
through the armature 25 amperes, its resistance 4 ohms. What is 
the applied E. M. F. ? Ans. 330 volts. 

12. A street car is propelled by two motors, driven from a battery 
of accumulators weighing 2£ tons, which is placed beneath the car 
seats ; the motors weigh 1 ton, the car 4 tons, the passengers aboard 
2 J tons, the efficiency of the motor is 80%. What power is supplied 
to the motors from the battery when the car is running on a level 
road at 8 miles per hour? Ans. 4942 watts. 

13. The street car, in problem 12, is required to ascend an 8 % 
grade at the reduced speed of 4 miles per hour. What is now the 
total power taken from the cells ? Ans. 20794 watts. 



LESSON XXX. 

ELECTRIC LIGHTING. 

The Electric Arc — Crater of the Arc — Types of Arcs — Eating of Arc 
Lamps — Arc Lamp Carbons— Arc Lamp Regulation — Inclosed 
Arcs — Alternating Current Arcs — Arc Lamp Circuits — Incan- 
descent Lamps — The Lamp Filament— Commercial Rating of In- 
candescent Lamps — Life and Efficiency of a Lamp — Incandescent 
Lamp Circuits — Potential Distribution in Multiple Lamp Circuits 
— Loss on Transmission Lines — Incandescent Wiring Calculations 
— The Three-Wire System — Motor Wiring Calculations — Ques- 
tions and Problems. 

371. The Electric Arc— When a current of from 6 to 10 
amperes, under a pressure of about 45 volts, is passed through 
two carbon rods, with their ends first in contact and after- 
ward gradually separated a short distance, as one-eighth inch, 
a brilliant arc of flame called the electric arc, is established 
between them. This arc is composed of carbon vapor ; that 
is, the high temperature caused by the passage of the cur- 
rent through the resistance of the contact surfaces causes the 
carbon to practically boil and the vapor thus arising, being a 
much better conductor than the air, conducts the current 
across the gap from one carbon tip to the other. This vola- 
tilization occurs chiefly at the end of the positive carbon 
terminal where the current enters the arc, and this point is 
also the seat of the highest temperature and maximum light- 
emitting power. As the arc is maintained across the gap, 
disintegration of the carbon takes place, the carbons waste 
away, and a cup-shaped depression, termed the crater, is 
formed in the positive carbon, while the tip of the negative 
carbon has a conical form, Fig. 379. The negative carbon 
being at a lower temperature than the positive, the vapor of 
the boiling carbon condenses upon its surface as pure 
graphite. Both carbons waste away, but the consumption of 
the positive carbon is about twice as rapid as that of the 
negative, since it is this carbon from which most of the vapor 
comes and part of which is re-deposited as graphite on the 
negative cone-tipped carbon. 

372. The Crater of the Arc— The light emitted by any 

415 



416 



PRACTICAL ELECTRICITY. 



heated body increases with its temperature. The temper- 
ature of the carbon in the crater, when in a state of ebullition, 
is about 3500° C, this being the hottest portion of the arc, 
and consequently the point from which - the most light is 

emitted. The intense heat in the 
crater will be realized when it is con- 
sidered that platinum (one of the 
most refractory metals, melting at 
1775° C), melts like wax when 
placed in the arc, and diamonds and 
many other substances are readily 
fused. About 12 per cent of the 
energy supplied to an electric arc 
appears as light, the balance being 
represented by ■ the heat evolved. 
About 85 per cent of the light 
emitted from an arc lamp is reflected 
from the crater, so that arc lamps are 
usually arranged with the carbons 
vertical and with the positive carbon 
above the negative, so that the light 
is reflected downward, the maximum 
illumination being in a zone sur- 
rounding the lamp at an angle of 
about 40° to the horizontal, and in- 
dicated by the arrows in Fig. 379. 
The amount of light emitted by an 
arc lamp is thus dependent upon 
the luminous area of the crater and 
this is dependent upon the number 
of amperes flowing through the arc ; the greater the area of 
the crater the greater the strength of current required to keep 
the increased area at the boiling point, since the temperature 
at which carbon boils, like that of other substances under 
constant pressure, is practically constant. A crater one inch 
in area emits, approximately, as much light as 100,000 
candles, but since its area depends on the quality of the 
carbon used, as well as the current, the crater area is not 
used as a standard of light. 

373., Types of Arcs. — When the electric arc is " struck " 
or " sprung " by bringing the carbon electrodes together and 
again separating them for a short distance, the arc possesses 




Fig. 379.— The Electric Arc. 

The white area in the positive car- 
bon represents the crater; the 
arrows indicate the direction 
of the maximum zone 
of illumination. 



ELECTRIC LIGHTING. 417 

peculiar characteristics depending upon the length of the gap 
between the ends of the carbons. When this distance is too 
small the arc will emit a peculiar hissing noise, and is then 
called a hissing arc. The noise is probably due to the too rapid 
volatilization of the carbon. An arc hisses when the current 
strength is increased beyond the practical limit for the size of 
carbon and particular length of the arc employed. When very 
powerful currents are used and the carbons are quite close 
together, a roaring of the arc occurs. Splattering sounds pro- 
duced by the arc are probably due to impurities in the carbon. 

When the distance between the carbons is increased 
slightly, a point is found where the arc burns quietly and 
steadily, and it is then termed a normal or silent arc ; if this 
distance be exceeded the arc flames. In a flaming arc, the 
light emitted is greatly decreased and the carbon consump- 
tion rapidly increased. The normal arc is a medium be- 
tween the hissing and the flaming arc and in commercial 
lamps, automatic regulation, % 376, is employed to feed the 
carbons as they are consumed, and thereby maintain the 
proper length of arc required for normal or silent burning. 
When the current is maintained constant the resistance of 
the arc varies directly as its length ; it will decrease as the 
area of conducting vapor is increased, and also as the tem- 
perature increases. 

374. Rating of Arc Lamps. — The ordinary commercial 
arc lamps are rated as equivalent to the light given by from 
1200 to 2000 candles. A lamp requiring 45 volts and 10 am- 
peres consumes 450 watts, and lamps are often rated in watts 
rather than candle power on account of the difficulties aris- 
ing in candle power measurements. Such a 450-watt lamp 
corresponds approximately to one rated at 2000 C. P., and a 
300-watt lamp, to one of 1200 C. P. The so-called 2000- 
candle power lamp emits from about 600 to 700 candle power 
in one direction in the zone of maximum illumination, Fig. 
379. The voltage used in practice varies from 45 to 47 volts 
drop across the arc, and the current, from 6 to 10 amperes, 
according to the amount of light required, a common value 
being 9.6 amperes and 47 volts at the arc. 

In search-light projectors much larger currents are used, 

as from 50 to 250 amperes, with voltages of from 47 to 53 

across the arc. The voltage at the terminals of an arc lamp 

will be greater than that across the arc, since there is some 

27 



418 



PRACTICAL ELECTRICITY. 



drop on the solenoids or magnets used in the lamp's regula- 
tion, % 376. 

375. Arc Lamp Carbons. — Carbon rods are generally 
used in arc lamps, and are composed of coke, tar, or the 
graphite deposited in the inside of retorts used for manufac- 
turing illuminating gas. The material selected is ground to 
a fine powder and mixed with some binder, as molasses, to 
make the particles adhere firmly; the mass is then molded 
to the proper form, baked, and finished. 

In cored carbons an inner core of soft carbon, having a 
higher conductivity than the solid carbon, tends to confine 
the current to the centre of the rod, and, con- 
sequently, the crater of the arc. In solid car- 
bons the crater travels around the end of the 
carbon, the current always tending to take 
the shortest path of least resistance ; with cored 
carbons the travel is reduced and the distribu- 
tion of light is more steady. From 3 to 6 volts 
less are required across the arc with cored car- 
bons, since the softer carbon volatilizes at a 
somewhat lower temperature. Carbons, copper- 
plated to within a short distance of the pointed 
end, last longer than when not so plated, and 
also offer less resistance to the flow of current 
through the circuit. The diameter of carbons 
is proportional to the current to be conducted, 
and is about 5-16 inch for a 6-ampere lamp and 
9-16 inch for a 10-ampere lamp. A 2000-C. P. 
lamp, having a positive carbon 12 inches in 
length and a negative carbon 7 inches in length, 
will burn about 9 hours. 

In an alternating current arc the crater alter- 
nates from one carbon to the other with each 
reversal of current, so that both carbons are con- 
sumed equally when the rods are horizontal. 
When vertical, the upper carbon will be con- 
sumed about eight per cent faster, owing to the 
action of the ascending currents of heated air. 

376. Arc Lamp Regulation. — After an arc is struck, and 
the electrodes separated for a fixed distance, the consumption 
of carbon gradually widens the gap until the resistance be- 
comes so high that the current will not pass when the lamp 




Fig 
Single Carbon 
Automatic Feed 
Arc Lamp. 

The arc is ex- 
posed to the air 
and the lamp 
trimmed nightly. 



ELECTRIC LIGHTING. 



419 



goes out ; to light it again the carbons must be brought into 
contact and then separated. In an automatic feeding lamp the 
carbons are moved together automatically as they are con- 
sumed, so that the length of the gap is maintained constant 
and consequently the distribution of light is continuous. 

A simple means for producing automatic feeding is depicted 
in Fig. 381 and embodies the principle involved in the con- 
struction of the Brush differential series automatic feed arc 
lamp. The two carbon rods are represented by E and F, and are 
connected in series with the series solenoid A, and to the main 



M 1 



: K- 



=fiftJS 



_3 i 5 ?* 1 ^ 

0+ O R 



Or 11 



2 C 



<D_ 



SHUNT COIL 



Bfi 



D 






SERIES COIL 



+ 
7/% 



M 



Fig. 



381.— Diagram of Connections of an Automatic Feed Differential Arc 
Lamp. — Clutch Type Pattern. 



supply line by the lamp terminal binding posts 3 and 4. The 
upper or positive rod, E, passes through a clutch, H, supported 
by the horizontal brass lever, DH, pivoted at C, and also 
fastened to an iron core, AB, at point D. The series solenoid is 
wound with a few turns of heavy wire of sufficient size to carry 
the total current flowing through the lamp. Directly above 
this coil is located the shunt solenoid B, of a much higher re- 
sistance than A, which is connected in shunt with the arc, 
across the points 1, 2. The action is as follows : the carbons 



420 PRACTICAL ELECTRICITY. 

are in contact until the current is turned on ; when current 
flows through the lamp from post 3, it divides at point 1 and 
flows mostly through the series coil circuit which is of lower 
resistance. The series solenoid is thus magnetised and draws 
the iron core, AB, downward, which motion raises the positive 
carbon a certain fixed distance and strikes the arc. As the 
lamp burns, the length of gap and its resistance increases, 
which shunts more current around the shunt solenoid, when 
at a certain instant, its attractive force for the iron core AB 
overcomes that of the series coil and the core is thus lifted up- 
ward by the shunt solenoid ; this action lowers the positive 
carbon to its former fixed distance, corresponding to the nor- 
mal length of the arc. The two coils thus work in opposition 
to each other, illustrating the differential principle, and the 
length of the arc is maintained practically constant. If for 
any reason the clutch at H should fail to release the upper 
rod, the resistance of the gap would continue to increase and 
an abnormal current, flowing through the shunt coil and the 
magnet, K, would attract its keeper. This action closes 
the switch, MN, which automatically cuts the lamp out 
of circuit and at the same time introduces a resistance, R, in 
parallel with the shunt coil to carry the current to other lamps 
operated in the same series circuit. When arc lamps are pro- 
vided with such an automatic cut out, and connected in series, 
there is no danger of interrupting the service by the failure of 
one lamp to properly burn. In double carbon lamps, when 
one set of carbons is consumed the other set is automatically 
switched into circuit and the period for which the lamp will 
give illumination is thus doubled. 

377. Inclosed Arcs. — When an arc is maintained in the 
open air the consumption of carbon is quite rapid ; for ex- 
ample, 1 \ inches of carbon per hour ; if, however, the arc is 
inclosed from the air, thereby diminishing the supply of 
oxygen for supporting perfect combustion, the consumption 
of carbon is much slower ; for example, 3-20 of an inch per 
hour, or the lamp may burn 150 hours without trimming. 
A small glass globe, about 6 inches long and 3 inches in 
diameter, is tightly fitted to the lower carbon, so that it 
passes up through the globe which is covered, at its upper 
end, with a corrugated iron washer having a central hole 
slightly larger than the diameter of the carbon rod used, 
thus permitting it to move freely. When the arc is struck 



ELECTRIC LIGHTING. 



421 



the available oxygen is soon exhausted and the bulb is then 
filled with a hot atmosphere of nitrogen, carbon monoxide, 
and carbon dioxide. The little oxygen which enters through 
the crevice between the upper carbon rod and the washer is 
very desirable, since it unites with the carbon to form a gas. 
If all the oxygen were entirely excluded the carbon would 
quickly be deposited on the inside of the bulb and interfere 
with the light. In time the bulb 
becomes coated on the inside with a 
light-colored deposit, due chiefly to 
impurities in the carbon ; it should 
then be replaced by a new one. In 
an inclosed arc the gap may be much 
longer, without a rapid combustion 
of carbon, since the oxygen is elimi- 
nated ; the potential at the arc is 
thus increased with its increased 
length to about 80 volts and the 
current of the average lamp de- 
creased to about 5 amperes. The 
chief advantages of inclosed arcs 
are the saving of carbon and the 
diminished cost of labor for trim- 
ming. An open-air arc is trimmed 
nightly and an inclosed lamp, prob- 
ably once every ten days. 

378. Alternating Current 
Arcs. — In arcs fed from an alter- 
nating current there is not a con- 
tinuous flame, but the arc is lighted 
and extinguished with each reversal 
of current. When the reversals are greater than 100 per 
second the flicker is not ordinarily noticeable. There is no 
crater, since each carbon acts as a positive at every other 
alternation, and the carbon consumption is nearly the same, 
*(\ 375. Cored carbons are always used in alternating current 
lamps to secure a sufficient supply of the carbon vapor to 
maintain the current's path at the instant the arc is ex- 
tinguished, when the current reverses. For this reason the 
current required for alternating current arcs must be larger 
than for direct current arcs, usually about 15 amperes, with 
30 to 35 volts drop across the arc. 




Fig. 382.— Single Carbon 

Automatic Feed Inclosed 

Arc Lamp. 

The arc is inclosed in the inner 

globe and the lamp will burn 

for 150 hours with one 

set of carbons. 



422 PRACTICAL ELECTRICITY. 

379. Arc Lamp Circuits. — Arc lamps are operated from 
constant potential or constant current circuits, and supplied 
by either direct or alternating currents. Special features of 
mechanical construction are embodied in the lamps accord- 
ing to the circuit from which they are to be supplied. When 
it is required to operate 45-volt series arc lamps from 1 10-volt 
constant potential circuits, two lamps are connected in series 
with sufficient extra resistance to give the proper drop across 
the lamps. Resistance is also added in series with inclosed 
lamps so that one lamp may be operated from a 1 10-volt 
constant potential main, or two in series, with extra resistance 
placed across 220 volts. Choke coils, % 298, are used to reg- 
ulate the current when the lamp is designed for A. C. cir- 
cuits. Arc lamps for street lighting service are usually oper- 
ated in series on constant current circuits because the lights 
are distributed over a large area and the energy can be much 
more economically supplied at a high pressure and a small 
current. For example, 100 arc lamps requiring 50 volts and 
10 amperes each, when connected in series, may be operated 
from a No. 6 B. & S. copper wire having a resistance of about 2 
ohms per mile. The resistance of a circuit 5 miles long is 
10 ohms and when carrying 10 amperes, the drop on the 
line is 100 volts, Formula (29), and the loss on the line 1000 
watts, Formula (62), or 1-K. W. The potential difference 
at the generator terminals will be 5100 volts. The total 
energy supplied to the lamps and line is 51 K. W. and the 
efficiency of transmission 98 per cent (50 -^ 51). To operate 
the same number of lamps from a low voltage constant po- 
tential multiple circuit, the dynamo must deliver 1000 
amperes, and for the same loss on the line the weight of cop- 
per would be more than 1000 times as great as that on the 
series circuit. See problem 91 , page 234, also ^j 348 and 353. 

380. Incandescent Lamps. — In an incandescent electric 
lamp the light is produced by heating to a state of incandes- 
cence, a high resistance solid conductor which is not readily 
fused by the passage of a current through it. A slender 
carbon thread, termed a, filament, is used as the conductor and 
is hermetically sealed in a vacuum in a glass globe, to prevent 
it from burning, ^f 97. Two platinum wires are sealed in the 
lower part of the glass bulb and are connected to the termi- 
nals of the filament, and their other ends, to two copper 
wires which make connection with the lamp base, Fig. 93, 



ELECTRIC LIGHTING. 423 

page 78. Platinum is used to pass through the glass because 
it expands and contracts at the same rate as the glass and 
the vacuum is thereby preserved at all times. The lamp 
base consists of two pieces of brass insulated from each other, 
secured to the lamp bulb by cement and arranged so as 
to hold the lamp securely when it is placed in a retaining 
socket connected to the main supply leads. By a switch in 
this socket, the current from the mains is turned off or on to 
the lamp as desired. 

381. The Lamp Filament. — The so-called "squirted fila- 
ments " are generally used in incandescent lamps. One type 
is made by dissolving cotton in a solution of zinc chloride 
which produces a viscous, semi-transparent liquid in which 
the fibrous appearance of the cotton almost disappears. 
This gelatinous material is forced or squirted through a 
small hole into a vessel of alcohol, which causes it to set and 
sufficiently harden for handling. After washing, the material 
resembles cooked vermicelli and is wound upon a drum and 
dried, when it possesses considerable strength and has the 
appearance of cat-gut string, such as used on a violin. It is 
then cut into suitable lengths and carbonized by being placed 
in a crucible surrounded by charcoal, so as to exclude the 
air, and then heated for several hours in a furnace. The 
effect of the carbonization is to drive off everything from 
the material but the carbon, which is left as a conducting 
thread. The filaments are then carefully measured as to 
their length and diameter, and assorted for the different sizes 
of lamps in which they are to be used ; the length of fila- 
ment is nearly proportional to the voltage, and the surface, 
to the candle power. 

The filaments are next treated by the " flashing " process, 
the object of which is to insure strength and uniformity in 
resistance. This is accomplished by inserting the filament 
in a closed vessel containing hydrocarbon gas and then rais- 
ing it to incandescence by passing an electric current through 
it. The action deposits carbon on the filament and if some 
points are of a higher resistance than others, their tempera- 
ture will be correspondingly higher and more carbon will be 
deposited at such places. Measuring instruments are inserted 
in circuit with the filament under treatment and the deposit 
continued until the desired resistance is attained. The fila- 
ment is then ready for mounting upon the platinum leading- 



424 



PRACTICAL ELECTRICITY. 




in wires and is secured to them by a paste of carbon and 
molasses. The platinum wires, P, are sealed in the end of a 
glass tube, A, Fig. 383, which is sealed into the blown glass 
bulb of the ordinary shape. The upper end of the bulb 

terminates in a glass tube which is 
connected to the air pump. After 
the proper degree of exhaustion this 
tube is heated and sealed leaving 
the pointed tip, T, on the end of the 
lamp. 

382. Commercial Rating of In- 
candescent Lamps.— After ex- 
haustion and sealing of the bulb the 
lamp is compared with a standard of 
illumination, while measurements of 
the pressure at its terminals and 
current flowing through it are made. 
The pressure is marked on each 
lamp, also the corresponding candle 
power and the watts consumption. 
The standard lamp in general use is 
rated as equivalent to the light given 
by 16 candles, and may consume 
from 50 to 60 watts. A 110-yolt 
55- watt 16-candle-power lamp re- 
quires .5 ampere, Formula (63) ; 
the hot resistance is therefore 220 
ohms, Formula (30) ; the watts per 
candle are 55-^-16 = 3.4 watts, or 
the candles per watt = 16 -*- 55 = 
.29. Lamps are usually made for 
50 to 60- volt, 110 to 11 5- volt and 
220- volt constant potential circuits ; a 16-C. P. lamp requir- 
ing 55 watts will therefore take 1 ampere on a 50-volt circuit ; 
.5 ampere on 110-volt; and .25 ampere on 220- volt circuit, 
the resistance of the filament increasing with the voltage 
when the candle power is constant. For any particular volt- 
age the higher the candle power of the lamp the larger the 
area of its filament, the less its resistance, and consequently 
the more current it will take. See page 151. A lamp should 
not be subjected to a voltage higher than its rating ; with a 
slight increase in pressure the brilliancy increases rapidly 



Fig. 383. — Incandescent Lamp 
and Retaining Socket. 



ELECTRIC LIGHTING. 425 

since the temperature rises with the increased current, and the 
life of the lamp is shortened. For example, if the filament 
of a 110- volt lamp has such a resistance that it will carry 
one-half ampere, without a dangerous rise in temperature ; 
when subjected to 220 volts the current through it is 
doubled and the heat is so intense as to destroy the fila- 
ment. A lamp supplied with 110 volts alternating current 
will give the same candle power as when supplied with 110 
volts direct current. 

383. Life and Efficiency of a Lamp. — After a lamp is 
in service for a period of time the carbon filament disinte- 
grates, or wears away, and there appears a blackened deposit 
upon the inside of the globe. The disintegration reduces the 
diameter of the filament, increases its resistance and conse- 
quently diminishes the current and the light from the lamp ; 
finally the filament breaks, and the lamp is said to have 
"burned out." The average life of the standard 16-C. P. 
lamp used in practice is from 600 to 800 hours, and even 
though the filament does not then break, the candle power 
falls off so rapidly with the disintegration that it is often 
cheaper to use a new lamp instead of the old one, which con- 
sumes current but gives little light. Tlie efficiency of a lamp 
is the ratio of the number of candles it will produce to the ivatts 
absorbed by it. A high efficiency in average use is about 3 
watts per candle when the life is about 800 hours. If the 
lamp is constructed with a large filament so as to give the 
same light at a reduced temperature, with 4 watts per candle, 
the life will be several thousand hours. The average 
efficiency used in practice is about 3.5 watts per candle. 
High efficiency lamps are suitable for mains where the 
pressure is very closely regulated, since the variation of two 
or three volts above the usual lamp voltage will materially 
shorten the life of the lamp. On the other hand, low efficiency 
lamps will not have such a rapid rise in temperature for a 
small variation in voltage and are therefore mostly used in 
cases where the supply voltage is not so closely regulated. 

384. Incandescent Lamp Circuits.— Incandescent lamps 
are usually operated from low voltage constant potential cir- 
cuits and supplied by direct or alternating currents. With a 
potential of 500 volts, as in street car service, the lamps are 
grouped in multiple series ; for example, 5 100-volt lamps in 
series, or 10 50- volt lamps in series being placed across the 



426 PRACTICAL ELECTRICITY. 

mains. A constant current series incandescent lamp system, 
for suburban street lighting, is sometimes employed, in which 
case automatic cut-outs connected to each lamp, preserve the 
continuity of the line in case any lamp burns out. Series 
incandescent lamps are introduced in arc circuits and are con- 
structed with very large filaments to carry from 5 to 10 am- 
peres ; the drop across the lamp is only a few volts ; for ex- 
ample, 6 volts for a 10-ampere 16-C. P. lamp. 

385. Potential Distribution in Multiple Lamp Circuits. 
— In a series circuit the drop on the lead wires does not in- 
terfere with the regulation of the voltage at the terminals of 
each lamp and the current being constant, the lamps burn at 
the normal candle power. In multiple circuits, however, the 
drop on the lead wires is an important factor and requires 
that the lamps be so distributed, and the size of the wire so 
proportioned, that each lamp will receive, approximately, the 
same voltage. For example, consider 200 110- volt incandes- 
cent lamps to be connected in parallel at various distances 
along a pair of mains extending 500 feet from the dynamo, 
and that the P. D. at the generator terminals is 112 volts; 
the lamps near the generator end of the mains will receive a 
higher potential than 110 volts and burn above candle power, 
with the result of frequent lamp renewals, while those near 
the distant end of the line will receive less than 110 volts and 
burn below candle power. In order to overcome this diffi- 
culty, centres of distribution are planned in wiring construction, 
and the lamps are grouped so as to be supplied from these 
centres. Feed wires are run from the generator to the points of 
distribution, and a constant potential maintained at these 
points by regulation at the generator. No lamps are connected 
to the feeders. Several sets of mains are run from these centres 
and supply sub-centres of distribution, to which the lead 
wires to the lamps are connected. The total drop or fall in 
voltage from the generator to the lamps in such a feeder and 
main system radiating from a central supply station, may be 
from 10 to 20 per cent of the generator voltage, so that the 
dynamo is run at a correspondingly higher voltage than that 
required by the lamps. For example, the size of conductors 
may be so proportioned that when carrying full load their re- 
sistance produces a drop of 10 volts on the feeders, 3 volts on 
each set of mains radiating therefrom, and 2 volts on each set 
of sub-mains. Such a system of sub-division of the trans- 



ELECTRIC LIGHTING. 



\Tl 



M 



2Z£ 



U 



5i-n=9 &^^ 



n 



£ 






Aff 



B 

n 



3^: 



5n5 0n — 13 



a 



i 



FL— J] 



It 

Fig. 384,— Plan for the Distribution of Potential in Electric Light Wiring 

of Either a House or Ceiling of a Factory by the Two-wire 

Multiple System. 

A, B, C are fusible cut-outs introduced wherever the size of wire changes. The thickness 
of the lines represents the relative size of the wire. 



428 



PRACTICAL ELECTRICITY. 



mitting conductors is worked out upon an elaborate scale for 
lighting large and compact areas, as in the house and store 
service of cities supplied from a central generating plant. In 
the wiring of a house for about 50 standard 110- volt 16-C. P. 
lamps, the drop in voltage, at full load, will be about 2 per 
cent of the pressure supplied at the service mains. Know- 
ing the current to be required by any feeder as, for example, 
that to the third floor for 20 lamps, about 10 amperes, the 
size of wire is readily calculated as in ^|^J 239 and 387. 
With an isolated plant in a large office building the drop may 
be 5 per cent of the generator voltage. In a building of 
20 floors, a pair of main feeders may be run from the gene- 
rator room to, say every 4 floors ; there will thus be 5 sets of 
feeders, each being calculated to supply the given current with 
a 5 per cent loss on the line. The feeders terminate in cut- 
outs arranged in junction boxes, and sub-feeders are carried 
to each of the four floors to be fed from one junction. Mains 
are run from these points to smaller local centers with a loss 
of from Ho 1 per cent allowed in calculations for these lines. 
386. Loss on Transmission Lines. — The weight of copper 
wire required for conducting current to lamps or motors, with the 
same loss on the transmitting line, is inversely proportional to the 
square of the voltage supplied to the lamps or motors. For ex- 
ample, suppose 50000 watts (50 K. W.) are transmitted to 
some distant centre of distribution ; 1000 watts the permiss- 
ible loss on the line ; the weight of copper required, when the 
energy is delivered at 50 volts, to be 1000 pounds ; then the 
comparative weight of copper for other voltages according 
to the above law is given as follows : 



Energy Transmitted. 


Loss on the Line. 


Copper 
Required. 


K.W. 


Volts. 


Amperes. 


Volts Drop. 


Amperes. 


Watts. 


Pounds. 


50 
50 
50 
50 


100 

200 

500 

1000 


500 

250 

100 

50 


2 

4 

10 

20 


500 

250 

100 

50 


1000 
1000 
1000 
1000 


1000 

250 

40 

10 



As the voltage, at which the above energy is transmitted 
increases, the current to be conducted on the line decreases, 
thereby decreasing the size of the wire, increasing its resist- 



ELECTRIC LIGHTING. 429 

ance and the line drop. As the drop on the line increases the 
current is proportionally reduced and the line loss the same. 

In the electrical transmission of power to long distances, 
economy of copper is attained by transmitting the energy at 
a very high voltage and reducing it to a working value, within 
the danger limit, at the receiving station. For example, 
several thousand horse power are transmitted from Niagara 
Falls to Buffalo, about 26 miles, at 20000 volts. The current 
is an alternating one, and at Buffalo the voltage is reduced 
by transformers to the proper values for lighting and power 
purposes. In a western transmission plant the power is 
transmitted at 80000 volts with a greater reduction in weight 
of copper but requiring special insulating materials for such 
a high potential. 

387. Incandescent Wiring" Calculations. — The simplest 
method for calculating the size of wire required to conduct 
current to any given number of lamps, with any permissible 
drop in voltage on the line, is to find the resistance of the 
line by Ohm's Law and then consult the wire gauge table and 
the table of safe carrying capacities, pages 113 and 266. See 
also «[[ 239. 

A general formula to find the size of wire directly in cir- 
cular mil area required to carry any direct current any dis- 
tance, with any given loss on the line, is derived by combin- 
ing Formulas (22) and (30) as follows : 

By Formula (22) R = ^^- • 

(30)K = g. 

Therefore ^ = g, 

and E X C. M. = K X L X C, 
orC.M. = KxLxC. 
hi 
Copper being generally used as the conductor, K = 10.79, and this 
formula becomes 

c M _1079X_L>CC 11Q 

E 

Where C. M. = circular mil area ; 

K = 10.79 = resistance 1 mil-foot of copper wire ; 
L = length of circuit in feet ; 
C = current in amperes ; 
E = volts drop on the line. 



430 PRACTICAL ELECTRICITY. 

To Find the Size of Copper Wire in Circular Mils, to 
Conduct any Given Direct Current, Any Distance With 
a Given Drop on the Line : 

Multiply the total length of the line, in feet, by the resistance 
of a mil-foot, 10. 79, and this product by the current, in amperes, 
to be conducted ; divide this product by the volts lost on the line. 
Formula (110). 

The circular mil area so found must be compared with the 
table of carrying capacities, page 266. By using a very ex- 
cessive drop on the line the circular mil area calculated by 
Formula (110) in some cases would be much too small for 
the current to be conducted, and hence the necessity of a 
check upon the calculations, by the table of carrying capaci- 
ties. Usually the distance from the generator to the centre of distri- 
bution is given for the two-wire multiple system, and this distance 
must be multiplied by 2 to obtain the total length of the circuit, 
L in Formula (110). 

Prob. 134 : One hundred 55-watt 110-volt lamps are connected in 
parallel and to a centre of distribution located 125 feet from the 
dynamo which generates 113 volts P. D. ; the potential at the dis- 
tributing centre is 111 volts. What size wire is required for the 
feeder ? 

W 55 

By Formula (63) C = -^ =tta == -5 ampere per lamp. 

100 X .5 = 50 amperes to be conducted. 
113 — 111 = 2 volts drop on the line. 
By Formula (110) C. M . = 10 - 79 X 125 X 2 X 50 =67437 c M 

L = 125 X 2 = 250 feet, C = 50 amperes, E = 2 volts. 

Consulting the table, page 113, the size of wire nearest to 
67437 C. M. is No. 2 B. & S. = 66370, which is smaller 
than that required. Always use the next larger size of 
wire to that calculated, or in this problem a No. IB. & S., 
which will give a little less drop than 2 volts. Consult 
the safe carrying capacity table, page 266, and it is found 
that No. 1 will carry 107 amperes, and will thus readily 
carry 50 amperes. A much smaller wire could have been 
used in this problem, as a No. 5, which carries 54 amperes, 
but the line drop and loss would then have been correspond- 
ingly larger, since the resistance of the circuit is increased. 
The line loss is a constant factor — that is, the watts, 50 X 
2 = 100, lost on the line in the above problem are constant, 
so long as this load is constant, and will cost each year a cer- 



ELECTRIC LIGHTING. 431 

tain sum for this loss, while the cost of the line installation 
is only the first cost. The most economical conductor is in- 
stalled when it is possible to make the yearly cost of the 
power lost on the lines equal to the interest on the value of 
the copper invested. The volts lost or drop on any circuit 
may be measured by a voltmeter, ^f 231, or calculated by 
Formula (29), when the current and resistance of the circuit 
are known, or from the following Formula, obtained by 
transposing Formula (110) : 

™ 10.79 XLxC M11 . 

E= — oi (111) 

To Find the Volts Lost or Drop in Any Circuit (of 
copper wire) : 

Multiply JO. 79 by the length of the circuit in feet, and this 
product by the current, in amperes ; divide this result by the 
circular mil area of the wire. 

Prob. 135 : An ammeter, connected in series with a circuit of cop- 
per wire 200 feet long, indicates 25 amperes ; the size of wire meas- 
ured by a wire gauge is No. 10 B. & S. What is the drop on the line ? 

By Formula (111) E = ^ X ^ X C = 10 -^ X 2 00><2_5 ==5 2 
volts. C. M. 10381 

To Find the Power Lost on Any Line : 

Multiply the volts drop on the line by the current flowing through 
it, W = E X C, Formula (62) . 

Prob. 136: (a) What power is lost on the line in Prob. 134? 
(b) What is the cost of this loss for 10 hours per day for 365 days at 
10 cents per kilowatt hour? 
By Formula (62) W = E X C = 2 X 50 = 100 watts (a). 
By If 223. 365 X 10 = 3650 hours X 100 watts = 365000 watt-hours. 
365000 ocr Tr w , 
ToOfT = 3 6 ° K - W.-hours. 

365 X.10 = $36.50 (b). 

388. The Three-Wire System. — In the three-wire multi- 
ple system two dynamos are joined in series, and the lamps 
connected between a centre or neutral wire joined to the junc- 
tion of the machines, and the positive and negative wires of 
the system, Fig. 385. When all the lamps are in circuit, 
Fig. 385, no current flows through the middle wire, and it 
can be disconnected at the generators without affecting the 
system. If only three lamps are connected on the No. 1 side 
of the system, then current for the two extra lamps not 
paired flows through the middle wire from the -j- brush of 



432 



PRACTICAL ELECTRICITY. 



No. 2 generator. The middle wire is now positive. If three 
lamps are out on the No. 2 side of the system, then current 
for the three lamps on the No. 1 side flows from the -f term- 
inal of generator No. 1 and returns to it by the middle wire, 
which is now negative. The middle wire, therefore, may have 
no current flowing through it, or current flowing in either one 
direction or the other, depending upon whether the lamps on 
both sides of the system are accurately balanced, which is the 
aim in practice. For this reason it is called the neutral wire. 
When all the lamps are turned off on one side of the system 




Fig. 385. — Incandescent Lamps Operated in Parallel from the 
Three- Wire System. 

the neutral wire carries the current for all the lamps on the 
other side. Motors wound for 220 volts are connected to the 
two outside wires and do not, therefore, interfere with the 
balancing of the system. 

The electromotive force is double that of the ordinary two- 
wire multiple system and the current required for any given 
number of lamps is reduced to one-half that required on the 
two-wire system. The chief advantage of the system is the 
saving effected in copper by its use, about f of the weight of 
copper being required, as compared with the two-wire system. 
For example, suppose 1000 pounds of copper are required for 
a given number of lamps operated from the 110-volt two-wire 
system. If the voltage be doubled, the weight of copper re- 
quired is J as much as before for the same loss, ^f 386, or 
250 pounds for the two wires. Now since in the three- wire 
system one extra wire is required, if it is made the same size 
as the others, as is often the case, it will weigh \ of 250 
pounds, or 125 pounds, and the three wires will weigh 375 
pounds, or only f of tire weight of copper is required by this 



ELECTRIC LIGHTING. 433 

system. The joint resistance of 10 110-volt, 220-ohm lamps 
on the two-wire system is 22 ohms, Formula (43), while on 
the three- wire system the joint resistance of the same number 
of lamps, two in series, 5 groups in parallel, is 88 ohms. 
The joint resistance of the lamps being four times greater on 
the three- wire system than on the two-wire system, the resist- 
ance of the lead wires will also be four times greater for the 
same percentage of loss, and therefore only one-fourth as 
as large as those required for the two-wire system. 

To Find the Size of Wire Required for the Three- 
Wire System : 

Find the size of wire required for the same number and kind of 
lamps on the two-wire system, by Formula {110), and divide the 
number of circular mils, so obtained, by £, Formula (112). 

C - M - = 10 - 79 4XE XC ( 112 >- 

Prob. 137 : The lamps referred to in Prob. 134, page 430, are to be 

operated from the three-wire system. What size of wire will be 

required ? 

x> i7 i /1-.OX n *r 10.79 X L X C 10.79 X125X2X50 
By Formula (112) C. M. = ^-^ = ^^ = 

16859 C. M. 
From Table VII, page 113, No. 8 B. & S. =16510 C. M. and from 
Table XV, page 266, No. 8 will carry 33 amperes. Since the current 
on the three- wire system is one-half that for an equivalent number 
of lamps on the two- wire system, the No. 8 wire in this problem will 
only carry 1-2 of 50, or 25 amperes, and is therefore sufficiently large. 
The neutral wire may be made the same size as the outside wires ; 
sometimes it is made one-half as large since it is hardly probable 
that all the lamps on one side of a well balanced three-wire system 
will be out and the others all burning. A further increased saving of 
copper is then attained. 

389. Motor Wiring Calculations. — To Find the Size 
of Wire, in C. M. , to Transmit any Given Horse Power 
any Distance, When the Voltage and Efficiency of the 
Motor Are Known : 

Multiply the rated horse power of the motor by 74-6 then by the 
length of the circuit in feet and then by 10.79 ; divide this result 
by the product of the voltage required by the motor and the drop on 
the line multiplied by the efficiency of the motor, Formula (US). 

Average motor efficiency. 

1 H. P 75 per cent. 

3 H. P. 80 " 

5 H. P 80 " 

10 H. P. . 90 " 

28 



434 PRACTICAL ELECTRICITY. 

Let E = voltage required by motor ; 

e = drop on the lines ; 
H. P. = horse power of motors ; 
% M = efficiency of motor, expressed as a decimal ; 
then from Formula (110) is derived, 

C m _ H.P.X7 4 6XLX10.79 

Prob. 138 : What size of wire is required to conduct current to a 220- 
volt 5-H. P. motor located 150 feet from the meter ; the drop on the 
line is to be 5 volts and the efficiency of the motor is 80% ? 

By *— (113) C. M. = H.P.XKg XLxM.T? = 

5 X746Xl50X2Xl0.7 9_-, Q7onr , M 
220- X 5 X. 80 i67Z{) U 1VL 

H. P. = 5, 80% = .80, L =150 X 2 = 300 feet, E == 220 volts, e == 
5 volts. 

From Table VII, page 113, No. 8, B. & S. == 16510 C. M. The mo- 
tor requires 21 amperes, calculated by Formula (114) in Prob. 139 ; 
and from Table XV, page 266, the carrying capacity is 33 amperes, 
so that No. 8 is the proper size of wire. 

To Find the Current Required by a Motor When the 
Horse Power, Efficiency, and Voltage are Known : 

Multiply the H. P. by 7^6 and divide this product by the voltage 
of the motor multiplied by its efficiency, Formula (111?). 
_ H. P. X 746 n , 

Prob. 139 : What current will the motor in Prob. 138 receive ? 
By Formula (114) C = ** *™ = _5_X_746_ = £1 ^^ 

H. P. = 5, E = 220 volts, %M = 80 = .80. 

To Find the Horse Power Developed by a Motor : 
Multiply the pressure applied to the motor terminals by the cur- 
rent supplied to it and multiply this product by the efficiency of the 
motor ; divide this result by 74.6, Formula (115). 

H. P. = C >< jj* »M . . (115). 

This formula is obtained by transposing Formula (114.) 

Prob. 140 : A current of 45 amperes is supplied to a motor, having 
an efficiency of 85 per cent, under a pressure of 220 volts. What 
horse power is developed by the motor ? 

By Formula (115) H. P. = C X ^* ^ M = 

45 X 220 X .85 = n H P 

746 
C = 45 amperes, E = 220 volts, %M = 85 = .85. 



ELECTRIC LIGHTING. 435 

QUESTIONS. 

1. What is the chief distinction between an arc and an incandes- 
cent lamp ? 

2. What is the crater of an arc, and where is it located? Give sketch. 

3. What is the relative consumption of carbon in a lamp used, (a) 
on direct current circuits ; (6) on alternating current circuits ? 

4. From what part of the arc is the most light emitted and what 
is the general direction of its reflection ? 

5. What is your answer to question 4 when the arc is fed by an 
alternating current ? 

6. What is the cause and disadvantage of a flaming arc ? 

7. What adjustment is required for an arc lamp which hisses badly? 

8. What is the advantage of cored carbons over solid carbons for 
arc lamps fed from alternating current circuits ? 

9. Why are arc carbons copper plated ? 

10. Why is the drop, in volts, across a normal arc between cored 
carbons less than when solid carbons are used? 

11. Describe the principle of action in a differential arc lamp? 
Give sketch. 

12. What is the difference between an inclosed and an open air arc ? 

13. State two advantages of the inclosed arc lamp. 

14. Why are arc lamps for street lighting generally operated in series? 

15. How are incandescent lamp filaments made? 

PROBLEMS. 

1. A 110-volt 16-C. P. lamp requires 55 watts. Give the following : 
(a) watts per candle; (b) candles per watt; (c) lamps per horse 
power; (d) lamps per K. W. Ans. (a) 3.4 watts per C. P. ; (6) .29 
candle per watt ; (c) 13 lamps per H. P. ; (d) 18 lamps per K. W. 

2. To transmit 300 K. W. a certain distance at 1000 volts, 900 
pounds of copper are required. How many pounds of copper will be 
required to transmit the same energy at 3000 volts, with the same loss 
on the line as before? Ans. 100 lbs. 

3. Two hundred 55-watt 110-volt lamps are connected in parallel 
and are fed from a centre of distribution located 100 feet distant from 
the generator ; 2\ volts are to be lost on the main feeders. What size 
of wire will be required ? Ans. No. B. & S. 

4. What power is lost on the feeder in problem 3 ? Ans. 250 watts. 

5. A series arc circuit, 5 miles in length, is constructed of No. 6 
B. & S. wire and carries 10 amperes, (a) How many volts drop on 
the line? (b) What power is lost on the line? (c) What is the 
yearly cost of the power lost on the line, running 10 hours a day for 
365 davs at 10 cents per K. W. hour? Ans. (a) 108.5 volts ; (6)*1085 
watts; (c) $396,025. 

6. The lamps in problem 3 are to be supplied from a three-wire 
multiple system. What size wire will be required ? Ans. No. 5 B. & 
S. (when checked by Table XV). 

7. With 6 volts drop on the line what size wire is required to carry 
current for a 10-H. P. 220-volt motor, located 150 feet from the source 
of supply ; efficiency 90 % ? Ans. No. 7 B. & S. 

8. What current will the motor in problem 7 receive ? Ans. 37 amp. 



APPENDIX. 

SUMMARY OF FORMULA. 

The following formulae have been derived in this book, and a problem solved to illus- 
trate the manner of using each one. 

In the text the formulas are referred to by numbers, so that the formula corresponding 
to any number desired is readily obtained from this summary, as is also the page where 
the formula is fully explained. 

Page Formula Number 

93. Q = C Xt (1). 

93. C = f (2). 

94. t = § ;.'■■ (3). 

* °-K^t ■ (4) - 

96. W= C X t X K (5). 

^ * = C^K (6) ' 

"• °=t*K (7) ' 

99. V = C X t XK (8). 

"• *=<nrr (9) - 

100 C- V XhX^73 (10) 

iw. u -.i733x76(273 + C°)Xt V ; 

inn v __ .1733xCX76( 27 3 + C°)Xt rn) 

1Ua V ~ h X 273 V h 

106. Microhms = ohms X 1000000 (12). 

., microhms n »\ 

106. Ohms^^^- • ■ (13). 

436 



APPENDIX. 437 

Page Formula Number 

106. M e g ohms = 1 ^ (14,. 

106. Ohms = megohms X 1000000 (15). 

109. R= 5 -j^ L CM)- 

ill. C. M. = d 2 (17). 

111. *=i/OM (18). 

112. Sq. mils = c X d (19). 

112. Sq. mils = C. M. X .7854 (20). 

112. C. M. = sq. mils X 1.2732 (21). 

ii4. R^to" (22j * 

114. L= BX K 0,M - (23). 

115. C.M. = -?^XK (24) 

C M 

115. Pounds per mile (bare copper wire )= -^V .... (25). 

C M 

115. Pounds per foot (bare copper wire) =AaKircoSj ■ (26). 

C 1VT 

115. Pounds per mile (bare iron wire) = nky( (27). 

119. C=| (28). 

121. E = CxR .. (29). 

122. R=| (30). 

123- = g-J_. (31). 

124. E = Cxr (32). 

124. E = C x(R+r) (33). 

124. R=|-r (34). 



438 



PRACTICAL ELECTRICITY. 



Tage 
124. 

130. 

130. 

131. 
132. 

136. 
136. 

140. 

141. 

141. 
142. 
143. 
145. 
146. 

147. 

147. 



Formula Number 

. . . . (35). 



Total internal resistance of cells in series — r X ns . (36). 
E x ns 



(r X ns) + R 

Total internal resistance of cells in parallel = — 

nq 

c=-*- - 



(37). 
(38). 

(39). 



nq 



R 



Total internal resistance of any combination of 

cells --^^ (40). 



nq 



E X ns 



r X ns 



nq 
fC = E X K ] 

E-° 



J.R. 



+ R 



nq 



nq 
R 



J.R. 

R = J. R. X nq 



C + d + C 2 etc. X J. R. 



f 

Multiplying power of a shunt (n) = « 

C 



Cg 



+ 1 



(41). 

(42). 

(43). 

(44). 
(45). 



J.R.^I^p! 1 ... (46). 



(47). 
(48) 
(49). 

(50). 



APPENDIX. 439 

Page Formula Number 

t-o C tand ,--.* 

173 ' cTtand; (51) - 

176. C=5_Xl xtand (52). 

177. C = Kxtand (53). 

193. Magnetising Force = C X T (54). 

193 c ^ Magnetising Force (55) 

193 T ^ Magnetising Force ^ 56 ^ 

C 

208. ^=x~^A Xr ! (57). 

212. Horse Power of a steam engine = 33000 ' ^^' 

213. J = E X C X t (59). 

213. J = C 2 X R X t (60). 

214. J=| 2 Xt (61). 

215. W = E X C (62). 

215. C=|r (63). 

215. E=^ (64). 

218. H.P. = ?^ (65). 

218. K.W.^*^ (66). 

218. Watts = K.W. X 1000 (67). 

220. W = C 2 XR . (68). 

220. W=^ (69). 

220. R=^ (70). 



440 PRACTICAL ELECTRICITY. 

Page Formula Number 

221. C = -\J|[ (71). 

221. R=^ (72). 

221. E = /W X R . - • (73). 

222. H.P. = ^~? (74). 

222 - H - P - = 746^R (75) - 

m E= H.P.X746 (76) . 

222 . = H.P.X746 (77). 

222 - R =HT^i6 ••• (78) - 

222. K.W. = <^ (79). 

222 - K - W ' = 1TO (80) - 

223. W=- (81). 

r 

224 . N = i2<W_x_r . . (82) . 

225. Eff. = ^- • (83). 

U + r 

225. E* = w ^ (84). 

236. C = E-P.D. (85). 

r 

236. P.D.=?-^ (86). 

236. r = E ^ PP - (87). 

tt i t. n/r n E. M. F. Standa rd X AD (9 >^ 

244. Unknown E. M. F. = x?j * ■ ' V s6 >• 



251. 



APPENDIX. 441 

page Formula Number 

„, „ . x v Res. of Standard X Drop on X faQ , 
250. Unknown Resistance X- Drop on Standard (89) ' 

i-Ki- 1 ) (90) - 

_ - . . „ ,. Res. of A X length C rQ1 % 

2oo. Resistance of D = le ngth TB 

258. Resistance of D=^-^ (92). 

A 

269. Heat Units (H) = .0009477 xExCxt (93). 

269. H = .0009477 C 2 R t (94). 

269. H = .0009477 X watts X seconds (95). 

269 - ° = .0009477° E X t • (96) ' 

269 - * = .0009477 H X E X C (97) ' 

270. C° = (F ° ~? 2) X 5 (98). 

y 

271. F°=^-^+32 (99). 

271. R x = (R x T X F° Rise) + R (100). 

271. R 1 = R— (R x T X F° Fall) (101). 

370. Elec. Eff. = r - , W , (102). 

W + w + w l 

E — £ 
398. C = (103). 

398. g=E-(Cxr) (104). 

399. W = gxC (105). 

402. Counter E. M. F. + (0 X r) = applied E. M. F. . . (106). 

4n - w = ^o£- S * 746 (107) ' 

412. W 1= %G 3 ^ q XTi X 746 (108). 



442 PRACTICAL ELECTRICITY. 

Page Formula Number 

413. Total watts required = W + W, (109). 

429. CM. = 1*™**** {110) , 

431 . E = 10 - 79 C X ^ X ° '.(HI). 

433. o.M. = ^£|^ (112). 

-• " ^NT/xS** (113) - 

iSi - G -WjM- ■■■■ (114) - 

434. H. P. = C X ^ * %M .(115). 

746 



MENSURATION. 

Some of the following formulae are often used in electrical calculations. 

Properties of The Sphere. 

Let d = diameter ; 

r = radius ; 

c = circumference ; 

71=3.1416. 
Then: 
Volume = |tt r 3 = 4.1888 X r 3 . 

Volume = | ;rd 3 = 0.5236 X d 3 . 

Volume = i^- = 0.01689 X c 3 . 

Volume = — d X area of the surface, 
b 

2 

Volume = — d X area of the great circle. 

o 

2 
Volume = -~ volume of the circumscribing cylinder. 

Volume = 0.5236 volume of the circumscribing cube. 

AREA OF THE SURFACE OF A SPHERE. 

Area == 4-r 2 = 12.5664 X r 2 . 
Area = rrd 2 = 3.1416 X d 2 . 

c 2 
Area = ^ = .3183 X c 2 . 

Area =dxc. 

Area = 4X area of the great circle. 

443 



444 PRACTICAL ELECTRICITY. 

Area = area of a circle whose d is twice d of sphere. 
Area = curved surface of the circumscribing cylinder. 
6 X volume 



Area = 



Eadius 



d 

RADIUS OP A SPHERE. 



3 volume = ^ f -^ 



\| in 



Eadius = A I = V . 07958 X area surface. 

Circumference == 1^6 tt 2 volume = 1^59. 21 76 X volume. 



Circumference = 


-V tz X area of surface. 


Circumference = 


area surface 
d 




The Circle. 


Circumference = 


7rd. 


Diameter = 


- = c X 0.31831. 

Tt 


Area = 


d 2 x j = .7854 X d 2 . 


Area == 


c 2 X .07958. 


Area = 


r 2 X 7T. 



Area = -r X circumference. 

4 



The Ellipse. 

Area = Product both d's X .7854. 



The Cylinder. 
Area = circumference X altitude plus area of both ends. 
Volume — area of base X altitude. 



APPENDIX. 



445 



Table XXIII. 

^Recapitulation. 

definitions of practical electrical units. 



Quantities 

to be 
Measured. 


Synonyms. 


Sym- 
bol. 


Name of 

Practical 

Unit. 


Comparative 
Values. 


Remarks. 
Fundamental or absolute or 

C. G. S. Units are : 
Centimeter (C) for Length. 
Gramme (G) for Mass. 
Second (S) for Time. 


Current. 


Strength. 

Intensity. 

Rate of Flow. 

Coulomb per 
Sec. 

Volume (obso- 
lete). 


C 


Ampere. 


Coulombs -v- 

Seeonds. 
Volts -=- Ohms. 


One Ampere deposits .0003- 
286 gramme, or .004991 
grain of copper per second 
on the plate of a copper 
voltmeter. 


Quantity. 


Ampere - Sec - 
ond. 


Q 


Coulomb. 


Amperes X 
Seconds. 


One hour = 3,600 seconds; 
hence one ampere-hour= 
3,600 ampere-seconds, or= 
3,600 coulombs. 


E lectromo- 
tive Force. 
Difference 

ofPotential. 


Pressure. 
Tension. 


EMF 
orE 


Volt. 


Amperes X 
Ohms. 

Joules -f- Cou- 
lombs. 


One volt=.933 standard Dan- 
iell cell (zinc sulphate of a 
density of 1.4 and copper 
sulphate of a density of 
1.1). 


Resistance. 




R 


Ohm. 


Volts -i- Am- 
peres. 


One legal ohm is the resist- 
ance of a column of pure 
mercury, 1 square milli- 
meter in section and 106 
centimeters long, at Cen- 
tigrade. 1 *r«eohin=l .00283 
legal ohms. 


Capacity. 




K 


Farad. 


Coulombs -5- 
Volts. 


The microfarad, one-mill- 
ionth of a farad, has been 
generally adopted as a 
practical unit ; the farad 
is too large a unit for prac- 
tical use. 


Power 
Activity. 


Electrical H.P 
Rate of doing 

Work. 
Effect. 
Work ^- Time. 


P 

orPw. 
or HP 


Watt. 
(Volt-am- 
pere). 


Volts X Am- 
peres. 

(Amperes) 2 X 

Ohms. 
(Volts)* -4- 

Ohms. 
Joules -r- 

Seconds. 


One watt = 7 £ s electrical 

horse power. 
One electrical horse power= 
volts X amperes 
746 
One electrical horse power = 
(amperes) 2 X ohms 
746 
One electrical horse power= 
(volts)* 
746 ohms 




PowerXTime. 


W 

or Wj. 


Joule. 
(Volt-cou- 
lomb. ) 


Watts X Sec- 
onds. 

Volts X Cou- 
lombs. 

(Amperes) 2 X 
Ohms X Sec- 
onds. 

(Volts) 2 X Sec- 
onds -;- Ohms 


One joule is the work done 
or heat generated by a 
watt in a second. 

One joule is the heat neces- 
sary to raise .238 gramme 
of water 1° C. ; or one 
joule = .238 calorie or 
therm. One joule = .7375 
foot-pound in a second. 



446 



PRACTICAL ELECTRICITY. 



S8 
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APPENDIX. 

Table XXV. 

Equivalents of Units of Area. 



447 





Square 
Millimet'r 


Square 
Centime'r 


Circular 
Mil 


Square 
Mil 


Square 
Inch 


Square 
Foot 


Square Millimeter 


1 


0.10 


1978.6 


1550.1 


.00155 


.0000108 


Square Centimeter 


100 


1 


197,861 


155,007 


155007 


.001076 


Circular Mil 


.000507 


.0000051 


1 


78540 


8 X 10- 7 




Square Mil 


.000645 


.0000065 


1.2733 


1 


.000001 




Square Inch 


645.132 


6.451 


1,273,238 


1,000,000 


1 


.006944 


Square Foot 


92,898.9 


928.989 






144 


1 



Table XXVI. 

Equivalents of Units of Volume. 





Cubic 
Inch 


Fluid 
Ounce 


Gallon 


Cubic 
Foot 


Cubic 
Yard 


Cu. Cen- 
timeter 


Liter 


Cubic 
Meter 


Cubic Inch 


1 


.554112 


.004329 


.000578 




16.3862 


.016386 




Fluid Ounce 


1.80469 


1 


.007812 


.001044 




29.5720 


.029572 




Gallon 


231 


128 


1 


.133681 


.00495 


3785.21 


3.78521 


.003785 


Cubic Foot 


1728 


957.506 7.48052 


1 .037037 


28315.3 


28.3153 


.028315 


Cubic Yard 


46,656 


25,852.6 201.974 


27 


1 


764,505 


764.505 


.764505 


Cubic Centimeter 


.061027 


.033816 


.000264 


1 
.000035 i 


1 


.001 


.000001 


Liter 


61.027 


1 
33.8160 .264189 


.035317 




1000 


1 


.001 


Cubic Meter 


61027 


33816 264.189 


35.3169 


1.3080 




1000 





448 



PRACTICAL ELECTRICITY. 



Table XXVII. 

Equivalents of Units of Weight. 





Grain 


Troy 
Ounce 


Pound 
Avs. 


Ton 


Milli- 
gram 


Gram 


Kilo- 
gram 


Metric 
Ton 


Grain 


1 


.020833 


.000143 




64.799 


.064799 


.000065 




Troy Ounce 


480 


1 


.068041 




31,103.5 


31.1035 


.031104 




Pound Avoird'pois 


7,000 


14.5833 


1 


.000447 




453.593 


.453593 


.000454 


Ton 




32,666.6 


2240 


1 






.001016 


1.01605 


Milligram 


.015432 


.000032 


.000002 




1 


.001 


.000001 




Gram 


15.4323 


.032151 


.002205 




1000 


1 


.001 




Kilogram 


15,432.3 


32.1507 


2.20462 


.000984 


1,000,000 


1000 


1 


.001 


Metric Ton 




32,150.7 


2204.62 


.98421 




1,000,000 


1000 


1 



Tables XXIV to XXVIII taken from Professor Sloane's Arithmetic by permission of 

the publisher. 



APPENDIX. 



449 



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450 



PRACTICAL ELECTRICITY. 



Table XXIX. 

Comparative Table of Gauges. 

Giving the respective diameter and area of each number. 





American Wire Gauge 
(Brown & Sharpe) 


Birmingham Wire Gauge 
(Stubs) 


Standard Wire Gauge 


Gauge No. 


Diameter 


Area 


Diameter 


Area 


Diameter 


Area 




Inches 


Cir'lar Mills 


Inches 


Cir'lar Mills 


Inches 


Cir'lar Mills 


7-0 
6-0 
5-0 

4-0 


0.4600 


211600. 


0.454 


206100. 


0.500 
0.404 
0.432 
0.400 


250000. 
215300. 
186600. 
160000. 


3-0 
2-0 
1-0 

1 


0.4096 
0.3648 
0.3249 
0.2893 


167800. 

133100. 

105500. 

83690. 


0.425 
0.380 
0.340 
0.300 


180600. 
144400. 
115600. 

90000. 


0.372 
0.348 
0.324 
0.300 


138400. 
121100. 
105000. 
90000. 


2 
3 
4 
5 


0.2576 
0.2294 
0.2043 
0.1819 


66370. 
52630. 
41740. 
33100. 


0.284 
0.259 
0.238 
0.220 


80660. 
67080. 
56640. 
48400. 


0.276 
0.252 
0.232 
0.212 


76180. 
63500. 
53820. 
44940. 


6 
7 
8 
9 


0.1620 
0.1443 
0.1285 
0.1144 


26250. 
20820. 
16510. 
13090. 


0.203 
0.180 
0.165 
0.148 


41210. 
32400. 
27230. 
21900. 


0.192 
0.176 
0.160 
0.144 


36860. 
30980. 
25600. 
20740. 


10 
11 
12 
13 


0.1019 
0.09074 
0.08081 
0.07196 


10380. 
8234. 
6530. 
5178. 


0.134 
0.120 
0.109 
0.0950 


17960. 
14400. 
11880. 
9025. 


0.128 
0.116 
0.104 

0.092 


16380. 
13160. 
10820. 
8464. 


14 
15 
16 
17 


0.06408 
0.05707 
0.05082 
0.04526 


4107. 

3257. 
2583. 
2048. 


0.0830 
0.0720 
0.0650 
0.0580 


6889. 
5184. 
4225. 
3364. 


0.080 
0.072 
0.064 
0.056 


6400. 
5184. 
4096. 
3136. 


18 
19 
20 
21 


0.04030 
0.03589 
0.03196 
0.02846 


1624. 
1288. 
1022. 
810.1 


0.0490 
0.0420 
0.0350 
0.0320 


2401. 
1764. 
1225. 
1024. 


0.048 
0.040 
0.036 
0.032 


2304. 
1600. 
1296. 
1024. 


22 
23 
24 
25 


0.02535 
0.02257 
0.02010 
0.01790 


642.4 

509.5 
404.0 
320.4 


0.0280 
0.0250 
0.0220 
0.0200 


784. 
625. 
484. 
400. 


0.028 
0.024 
0.022 
0.020 


784.0 
576.0 
484.0 
400.0 


26 
27 
28 
29 


.01594 

.01420 

0.01264 

0.01126 


254.1 

201.5 
159.8 
126.7 


0.0180 
0.0160 
0.0140 
0.0130 


324. 
256. 
196. 
169. 


0.018 
0.0164 
0.0148 
0.0136 


324.0 
269.0 
219.0 
185.0 


30 
31 
32 
33 


0.01003 
0.008928 
0.007950 
0.007080 


100.5 
79.70 
63.21 
50.13 


0.0120 
0.0100 
0.0090 
0.0080 


144. 
100. 

81. 

64. 


0.0124 
0.0116 
0.0108 
0.0100 


153.8 
134.6 
116.6 
100.0 


34 
35 
36 
37 


0.006305 
0.005615 
0.005000 
0.004453 


39.75 
31.52 
25.00 
19.83 


0.0070 
0.0050 
0.0040 


49. 
25. 
16. 


0.0092 
0.0084 
0.0076 
0.0068 


84.64 
70.56 
67.76 
46.24 


38 
39 
40 
41 


0.003965 
0.003531 
0.003145 


15.72 j 
12.47 

9.888 : 






0.0060 
0.0052 
0.0048 
0.0044 


36.00 
27.04 
23.04 
19.36 



APPENDIX. 



451 



TABLE XXX .-DECIMAL EQUIVALENTS 

Of Eighths, Sixteenths, Thirty-Seconds and Sixty-Fourths 
of an Inch. 



Eighths. 


Thirty-Seconds. 


Sixty-Fourths. 


Sixty-Fourths 


% = -125 


^ = .03125 


B 5 5 = .015625 


|| = .515625 


34 = .250 


^ == .09375 


A = -046875 


M = .546875 


% = .375 


3 B , = .15625 
^=.21875 


£ = .078125 / 


|| = .578125 


X = -500 


& = .109375 


If = .609375 


% = .625 


^ = .28125 


£ = .140625 


|£ = .640625 


% = -750 
% = .875 


^ = .34375 


it = .171875 


B | = .671875 


H = .40625 


B | = .203125 


|| = .703125 


Sixteenths. 


if = .46875 


i| = .234375 


|| = .734375 


tf = .53125 


B | = .265625 


|| = .765625 


xV = .0625 


if = .59375 


|| = .296875 


|| = .796875 


, 3 B = .1875 


§£ = .65625 


U = -328125 


|| = .828125 


T 5 B = .3125 


§f = .71875 


If = .359375 


|| = .859375 


/ B = .4375 


|f = .78125 


|| = .390625 


|| = .890625 


T 9 B = .5625 


§£ = .84375 


|| = .421875 


|| = .921875 


U = .6875 


|f = .90625 


|| = .453125 


II = .953125 


TR = .8125 


f J = .96875 


|£ = .484375 


13 = .984375 


T | = .9375 









TABLE XXXI. 

Volts Lost on Copper AY ire. 

Table of volts lost or drop per ampere per 1,000 feet of conductor. (Calculated by 
E = C X B. Formula (29).) Copper wire, B. & S. gauge (70° F.). 



Size, 


Volts Drop per Ampere 


Size, 


Volts Drop per Ampere 


B. & S. 


per 1,000 Feet. 


B. & S. 


per 1,000 Feet. 


0000 


.0493 


17 


5.088 


000 


.0621 


18 


6.415 


00 


.0783 


19 


8.089 





.0987 


20 


10.20 


1 


.1242 


21 


12.86 


2 


.1570 


22 


16.22 


3 


.1980 


23 


20.45 


4 


.2496 


24 


25.79 


5 


.3148 


25 


32.52 


6 


.3970 


26 


41.01 


7 


.5006 


27 


51.72 


8 


.6312 


28 


65.21 


9 


.7958 


29 


82.23 


10 


1.040 


30 


103.7 


11 


1.266 


31 


130.7 


12 


1.596 


32 


164.9 


13 


2.012 


33 


207.9 


14 


2.537 


34 


262.2 


15 


3.200 


35 


330.6 


16 


4.035 


36 


416.8 



Problem. — How many volts would be lost in carrying 10 amperes a distance of 
2,000 feet on a No. 6 B. & S. Wire? 

Solution, from Table XXXI: .3970 volt is lost per ampere per 1,000 feet, or .7940 
volt per 2,000 feet for one ampere, or 7.9940 volts per 10 amperes, E = C X R. 



452 PRACTICAL ELECTRICITY. 

Table XXXII. 
Useful Equivalents for Electric Heating Problems. 

By H. Ward Leonard, Elec. Eng. 



Unit. 


Equivalent Value in other Units. 


Unit. 


Equivalent Value in other Units. 


t 
K. W. 

Hour «= 


1,000 Watt hours. 

1.34 horse power hours. 
2.656,400 ft. lbs, 
3,600,000 joules. 
3,440 heat units. 
366.848 kilogTam metres 

229 lbs. coal oxidized with 
perfect efficiency. 
3 lbs. water evaporated at 
212° F 
22.9 lbs. of water raised from 
62° to 212° F' 
8 cent's at usual rates for 
electric Heating. 


Ft. Lb. = 


1 .36 joules. 
1383 k. g. m. 
.000000377 K. W. hours. 
.000291 heat units. 
0000005 H. P. hour. 


1 

Watt = 


1 joule per second. 
00134 H. P. 
001 K. W ' 
3.44 heat units per houi 
73 ft. lbs. per second 
003 lbs. of water evapor- 
ated per hour 
44.24 ft. lbs. per minute 


1 Watt per 
Sq. In. = 


8.26 thermal units per sq. ft. 

per minute 
120° F above surrounding air 

(Japanned cast iron 

surface.) 
66° C- above surrounding air 

(Japanned cast iron 

surface.) 


1 
H. P 

Hoar = 


.746 K. W hours. 
1,980,000 ft. lbs. 

2,580 heat units. 
273.740 k. g. m. 

172 lbs. coal oxidized with 
perfect efficiency. 
2.25 lbs. water evaporated at 

212° F 
17.2 lbs. water raised from 62° 

F. to 212° F 
6 cents at usual rates for 
electric heating. 


1 
Heat Unit = 


1,048 Watt seconds. 
772 ft. lbs. 

.252 calorie (Kg.-d.) 
108 kilogram metres. 
000291 K. W hour 
000388 H. P hour 
0000667 lbs. coal oxidized. 
00087 lbs. water evaporated 
at 212° F 


1 
K. W. = 


1.000 Watts. 
1.34 H. P. 
2,656,400 ft lbs. per hour 
4,424 ft. lbs. per minute 

73.73 ft. lbs. per second 
3,440 heat units per hour 
573 heat units per minute 
9.55 heat units per second. 
229 lbs. coal oxidized oer 
hour. 
3 lbs. water evaporated per 
hour at 212° F 


1 Heat Unit 
per Sq. Ft. 
per min. — 


121 Watts per square inch. 
0174 K W 
0232 H. P 


1 Kilogram 

Metre 


7.23 ft lbs. 
00000306 H P. hour 
00000272 K. W hour 
0092 heat units \ 


1 Lb. Bitu. 
minonsCoal 

Oxidized 
with perfect 

efficiency = 


15,000 heat units. 

.98 lbs. Anth'cite coal oxi- 
dized. 
2.1 lbs. dry wood oxidized. 
15 cu. ft. illuminating gas. 
4.37 K. W hours (theoretical 

value.). 
5 81 H P hours (theoretical 
value ) 
11,590,000 ft lbs. (theoretical value.) 
13.1 lbs. of water evaporated 
at 212° F 


,1 

H. P. «= 


746 Watts. 
746 K W. 
33,000 ft lbs per minute 
550 ft. lbs. per second. 
2,580 heat units per hour. 
43 heat units per minute 
71 heat units per second. 
.172 lbs. coal oxidized per 
hour. 
2.25 lbs. water evaporated 
per hour at 212° F 


1 Lb. Water 

Evaporated 

212° F = 


.33 K. W. hour 
.44 H. P. hour 
1,148 heat units. 
124,200 k. g m. 
1,21 9,000 joutes. 
887.800 ft. lbs. 

076 lbs. of coal oxidized. 


I 
Joule «= 


1 Watt second 
00000278 K. W. hour 
102 k. g m. 
00094 heat units. 
73 ft. lbs. 



INDEX 



(Figures refer to the numbered pages.) 



A. 
Accumulator, 

Commercial, 84. 

Direction of current in, on 
charge and discharge, 84. 

Principle of, 83. 
Alternating current, 294, 337. 

dynamos, 376. 

from a direct current arma- 
ture, 349. 

Graphic representation of, 340. 
Alternator, Magneto, 342. 
Alternations, To find the number 

of, in a dynamo, 338. 
Amalgamation, 62. 
Ammeter, Balance beam, 202. 

Connecting, in circuit, 201. 

Connections for a shunted, 207. 

Dead beat, 178, 200. 

Dynamometer, 286. 

Gravity, 201. 

inclined coil, Thomson, 203. 

Increasing the range of read- 
ing of, 208. 

shunt, Weston, 206. 

Use of tangent galvanometer as 
an, 176. 

Weston, 203. 
Ammeters, Resistance of, 150. 
Ampere, Definition of, 92. 
Ampere-hour unit, 94. 
Ampere-hours, 

To find number of, consumed 
by apparatus, 94. 
Ampere meters, 200. 
Ampere-turns, 192. 
Anion, 80. 
Anode, 80. 
Arc, 

Alternating current, 418, 421. 

Crater of, 415. 

Flaming, 417. 

Hissing, 417. 

Inclosed, 420. 

Light from, 416. 

projectors, Current required 
for, 417. 



Silent, 417. 

Temperature of, 416. 

The electric, 415. 
Arcs, 

Types of, 416. 
Ai-c lamp, 

Automatic cut-out for, 420. 

Brush, 419. 

Candle power of, 417. 

carbons, 418^ 

circuit, Fall of potential in, 234. 

circuits, 422. 

differential, Principle of, 419. 

Inclosed, 420. 

regulation, 418. 
Arc lamps, 

Measuring resistance of, while 
burning, 248. 

Rating of, 417. 
Arc lighting, 

Dynamos for, 353. 
Armature, 

Active wire on, 351. 

Battery analogy of induced 
E. M. F. in a ring, 348. 

circuits, Multipolar field, 374. 

Brush arc light, 353. 

Closed coil, 352. 

coil, The act of commutation 
of, 364. 

connected on the quarter, 366. 

core construction, 355. 

core insulation, 357. 

core loss, hysteresis, 361. 

cross-connected, 374. 

Dead wire on, 351. 

Drum-wound ring, 352. 

Gramme ring, 346. 

Induced E. M. F. in a ring, 347. 

Multi-coil, 345. 

reactions, 362. 

resistance, 348. 

Shuttle, 342. 

Siemens drum, 350. 

Single coil, 345. 

Tooth core, 352, 356. 

453 



454 



INDEX. 



Armature, 

winding, 359. 
Armatures, 

Advantages of drum and ring, 
351 

Eddy current loss in, 355. 

Open-coil, 352. 

Pole pieces and, 38. 

Resistance of, 151. 
Astatic needles, 48. 



Blasting, Electric, 273. 
Barlow's wheel, 279. 
Battery, 

Amalgamation of zinc for, 62. 

Bichromate, 65. 

Bluestone, 69. 

Bunsen, 68. 

Carbon Cylinder, 72. 

Chemical action in a simple, 57. 

Chloride of silver, 74. 

circuit, Ohm's Law applied to, 
122. 

Closed circuit, 62. 

Crow-foot, 69. 

Daniell, 69. 

Definition of, 59. 

depolarizer, 64. 

Double fluid, 64. 

Dry, 75. 

Edison-Lalande, 73. 

Efficiency of a, 224. 

E. M.E., On what it depends, 
59. 

Fuller bichromate, 66. 

Gonda Leclanche, 72. 

Gravity, 69. 

Grenet, 65. 

Grove, 68. 

Internal resistance of, 116. 

Leclanche, 71. 

Leclanche, Directions for set- 
ting up, 71. 

Local action jn, 61. 

Open circuit, 63. 

Parts of, 55. 

Partz acid gravity, 67. 

polarization, 58. 

polarization, Remedies for, 63. 

Primary, 63. 

Recuperation of, 59. 

Simple voltaic, 52. 

Size of, 125. 

Smee, 64. 

solution, Bichromate, 66. 

Student's experimental, 61. 

Student's Daniell, 70. 



Battery. 

Why the hydrogen appears at 
the copper plate in, 58. 
Batteries, 

Chemicals and chemical sym- 
bols for, 76. 

Classification of, 75. 

Current strength from any 
combination of, 136. 

in parallel, Advantage of, 132. 

in parallel, Current from, 132. 

in parallel, Internal resistance 
of, 131. 

in parallel or multiple for quan- 
tity, 128. 

in multiple-series, 134. 

in opposition, 136. 

in series, Advantage of, 133. 

in series, Current from, 130. 

in series, E. M. F. of, 64. 

in series, to increase the E. M. 
F., 126. 

in series, Internal resistance of, 
130. 

Internal resistance of any com- 
bination of, 135. 

Power from, 223. 

Resistance of, 150. 

Table of E. M. F.'s of, 118, 
Brushes, 338, 356. 

Causes of sparking at, 367. 

Carbon and copper, 364. 

of a motor, Position of, 397. 

Position of, in a dynamo, 365. 

Shifting position of, 366. 



Carbons, 

copper plated, 418. 

Cored, 418. 

for arc lamps, 418. 
Carrying capacity of conductors, 

Safe, 265. 
Cathion, 80. 
Cathode, 80, 326. 
Cautery Electric, 273. 
Cell (See also battery) . 
Cells, Comparison of the E. M. F. 
of, by the potentiometer, 243. 

Number of, required for maxi- 
mum economy, 223. 

Power from, 223. 
Choke coils, 312. 
Collector rings, 338. 
Coherer, 332. 
Commutation 

of an armature coil, The act of, 
364. 

The act of, 344. 



INDEX. 



455 



Commutator 

construction, 358. 

for an open-coil armature, 353. 

Simple two-part, 343. 
Compass, Mariner's, 44. 
Condenser, Action of, with an in- 
duction coil, 318. 
Conductance defined, 103. 

of a circuit, 140. 
Conductors and insulators, 54, 104. 

Table of insulators and, 105. 
Conductivity method for calculat- 
ing resistance, 143. 

Table of, for metals, 115. 
Controller, Series-parallel, 408. 
Conservation of energy, 216. 
Consequent poles, 32, 188, 373. 
Cooking, Electric, 273. 
Correlation of energy, 216. 
Coulomb, Definition of, 92. 
Counter E. M. F. of a motor (See 

Motor). 
Circular mil, 

area, Calculation of, 111. 

defined, 110. 
Circuit 

Application of Ohm's Law to, 
123. 

breaker, 187. 

Definition of, 53. 

Division of current in a di- 
vided, 144. 
Circuits, Current in branches of 
multiple, 145. 

Inductive and non-inductive, 
312. 

Magnetic, 36, 187. 

Potential difference in multi- 
ple, 145. ' 
Current, 

Alternating, 77. (See also Al- 
ternating Current) . 

Chemical effect of, 79. 

Chemical generation of, 50. 

Continuous, 52, 77. 

deflects magnetic needle, 51. 

Direction of, 54. 

Division of, in a divided cir- 
cuit, 144. 

Direct, 318. 

direct, Graphic representation 
of, 345. 

Effects of, 77. 

effects, Variation of, through 
dissimilar apparatus, 91. 

Extra, of self-induction, 309. 

Heating effect of, 77, 265. 

How the effects vary with, 88. 

Inverse, 318. 

Magnetic effects of, 78. 



Current, 

Measurement of the strength 
of, 91. 

Measurement of, by a gas volta- 
meter, 98. 

of electricity, 50. 

pressure and resistance, Varia- 
tion of, 235. 

Pulsating, 77. 

Strength of, 87, 92. 

To find quantity of, flowing 
through a circuit, 93. 

Unit quantity of, 92. 

Variation of, and current's ef- 
fects, 87. 

wave, 341. 
Currents, Eddy, 306. 

in angular conductors, 283. 

induced in a wire bv a magnet, 
293. 

induced, To find the direction 
of, 295. 

induced in a coil by motion of 
a magnet, 296. 

induced, Lenz's law of, 297. 

induced by making or break- 
ing the primary circuit, 300. 

induced by moving either the 
primary or secondary circuit, 
300. 

induced by altering the 
strength of the primary cur- 
rent, 301. 

induced by reversing the direc- 
tion of the primary current, 
302. 

induced by moving the iron 
core, 302. 

induction, Table of, 302. 

Laws of parallel and angular, 
282. 

Magnetic fields of parallel, 280. 

Test on effects of, 90. 
Current-carrying capacity of cop- 
per wires, 266. 
Current-carrying wire, 

Automatic twisting of, around 
a pole, 277. 

Direction of magnetic field 
around, 154. 

Reaction of, on a magnet, 276. 

Rotation of, around a magnetic 
pole, 278. 

Rule for direction of magnetic 
field around, 159. 
Current strength, 

from any combination of bat- 
teries, 136. 

Calculation of, 119. 

Measurement of, 200. 



456 



INDEX. 



Current strength, 

Methods of varying, 125. 

To find average, 93. 

To calculate an unknown, 95. 

used in practice, Value of, 101. 
Cut-outs, Fuses and, 272. 
Cycle, 340. 

D. 

Dip, Magnetic, 44. 

needle, 12. 
Dynamometer ammeter, Portable, 
286. 

Siemens, 285. 

wattmeter, 286. 
Dynamo, 

Alternating current, 338. 

and motor. Comparison be- 
tween, 393, 399. 

brushes. (See Brushes.) 

Capacity of, 367. 

Compound wound, 375. 

Constant current, 384. 

Constant potential, 380. 

Definition of, 334. 

Double current, 350. 

Efficiency of, 369. 

equalizer, 389. 

Experimental motor and, 339. 

Faraday's disc, 307. 

Losses in a, 369. 

Magneto, 375. 

Parts of, 335. 

On what the induced E. M. F. 
of, depends, 303, 342. 

Over-compounded, 386. 

regulation, Series, 385. 

regulation, Shunt, 381. 

Self-exciting, 375. 

Separately excited, 375, 376. 

Separate coil, self-contained, 
376. 

Series, 376. 

Series and long shunt, 376, 387. 

Series and short shunt, 376. 

Series and separately excited, 
376. 

series, Action of, 384. 

series, Potential difference at 
terminals of, 368. 

Shunt, 376. 

shunt, Action of, 381. 

shunt, Principle of, 380. 

shunt, Potential at terminals 
of, 368. 

Simple direct current, 342. 

Simple type of, 336. 

Test on 1.25-K. W.,383, 388. 

To find the neutral point of, 365. 



Dynamos, 

Classification of, 336. 

Classification of, according to 
their field excitation, 375. 

Commercial rating of, 368. 

compound, Connections for two, 
in parallel, Plate II. ■ 

Compound, 386. 

Constant current, 375. 

Constant potential, 375. 

in parallel, Compound wound, 
389. 

Self-exciting principle of di- 
rect current, 378. 

shunt, in parallel, Connecting, 
382 

Table of E. M. F.'s of, 119. 

E. 

Earth, Polarity of, 41. 
Earth's Magnetism. (See Magnet- 
ism.) 
Eddy currents, 306. 
Eddy current loss in armatures, 355. 
Efiiciency, Commercial, of a dyna- 
mo, 370. 

Electrical, of a dynamo, 369. 

of a battery, 224. 

of a motor, 410. 

of power transmission, 397. 
Electrical effects, 49. 
Electric Waves, 50, 330. 
Electricity, Nature of, 49. 
Electrification, 52. 
Electrodes, Poles, plates and, 54. 
Electro -chemical series, 60. 
Electrodynamics, 280, 284. 
Electrolysis, 

Definition of, 80. 

of water, 79. 

of copper sulphate, 80. 

of lead acetate, 82. 

of zinc sulphate, 81. 
Electrolyte defined, 80. 
Electrolytic interrupter for spark 
coils, Wehnelt, 321. 

meter, Edison, 81. 
Electromotive force and potential 
difference, 228. 

Calculation of, 121. 

Generation of, 118. 

induced in a ring armature, 
347. 

induced, Upon what factors the 
value of, depends, 296. 

induced, Variation of, with the 
rate of change of the mag- 
netic lines of force, 303. 

Measurement of, 236. 



INDEX. 



457 



Electromotive force, 
of a battery, 59. 
of batteries, 64. 
of batteries and dynamos, 118. 
of batteries, Comparison of, by 

the potentiometer, 243. 
of a motor, Counter, 397. 
Electromagnet, Testing the attract- 
ive force of an, 195. 
Definition of, 185. 
Magnetic field of an, 186. 
Polarity of, 184. 
Coarse and fine wire, 195. 
Typical forms of, and their 
uses, 189. 
Electromagnetism, 50, 153. 
Electromagnetic induction, 293. 
Electroplating, Process of, 82. 
Electrostatics, 49. 
Electrotyping, Process of, 82. 
Energy, Relation between mechani- 
cal and electrical, and heat, 
270, 449. 
Equalizing bar, 390. 
Equivalents of mechanical and 
electrical work, 216, 449. 

F. 

Faraday's law of electromagnetic 

induction, 303. 
Field excitation, Classification of 
dynamos according to their, 
375. 
Field discharge, 310. 

magnets, Bipolar, 372. 
magnets, Multipolar, 373. 
rheostat, 381. 
Fluoroscope, Fluorescing screen 

and, 326. 
Foot-pound, Definition of, 210. 
Force, Definition of, 209. 

Different kinds of, 209. 
Formula?, Electrical power, 222. 
Mensuration, 443. 
Summary of, 436. 
Fuses and cut-outs, 272. 
Fusing point of various sizes of 
wire by 100 amperes, 273. 

G. 

Galvanometer, Astatic, 179. 
Ballistic, 179. 

Construction of student's de- 
tector, 169. 
D'Arsonval, 181. 
Deat-beat, 178, 200. 
Detector, 55, 169. 
Differential, 179. 



Galvanometer, 

long and short coil, The use 

of, 169. 
Principle of the, 167. 
Relative calibration of, 171. 
shunted, To find the current 

through, 147. 
Tangent, 172. 
tangent, Directions for setting 

up student's, 175. 
tangent, Student's combina- 
tion, 174. 
tangent, Table of constants for, 

176. 
tangent, Use of, as an ammeter, 

176. 
Thomson mirror-reflecting, 177. 
Galvanometers, Classification of, 
170. 
Resistance of, 150. 
Gas Voltameter (See Voltameter). 
Geissler tubes, 324. 
Generator (See Dynamo). 



H. 



Heat and work, 215. 

Electrical development of, 265. 
Electrical equivalent of, 268. 
Laws of the electrical develop- 
ment of, 267. 
Mechanical equivalent of, 217. 
Relation between mechanical 
and electrical energy and, 
270. 
unit, British thermal, 268. 
units, Calculation of electrical, 
269. 
Heating of conductors and their 
safe carrying capacity, 265, 
266. 
effects of the current, 77. 
Useful equivalents of electrical, 
452. 
Helix and solenoid, The, 162. 
Henry, Definition of the, 311. 
Horse power, Electrical, 217. 
Mechanical, 211. 
of a steam engine, 211. 
Hydraulic analogy to illustrate 

"volts lost," 228. 
Hysteresis, 308, 361. 



Impedance and reactance, 311. 
Incandescent lamp, 

Candle power of, 424. 

circuits, 425. 



458 



INDEX. 



Incandescent lamp, 

circuits, Potential distribution 
in multiple, 426. 

Commercial rating of, 424. 

Construction of, 78, 422. 

Life and efficiency of, 425. 

filament, Manufacture of, 423. 
Incandescent lamps, 

Measuring the resistance of, 
while burning, 248. 

Resistance of, 151. 

wiring, 426, 428. 

wiring calculations, 429. 
Inductance, 310. 
Induced currents (See Currents). 

E. M. F. (SeeE. M. F.). 
Induction coil, Action of, 317. 

Action of condenser with, 318. 

or transformer, Principle of, 
315. 
Induction coils, Construction of, 
320. 

Wehnelt electrolytic interrup- 
ter for, 321. 

Primary and secondary of, 297. 
Induction currents (See also Cur- 
rents) . 

currents, Classification of, 299. 

currents, Table of, 302. 

Electromagnetic, 293. 

Extra current of self-, 309. 

Faraday's law of electromag- 
netic, 303. 

Magnetic, 194. 

Mutual, 308. 

Self, 308. 

self-, Neutralizing the effects 
of, 312. 
Inductive and non-inductive cir- 
cuits, 312. 
Insulation, Breaking down of, 359. 

of armature cores, 357. 

test, 359. 
Insulator defined, 103. 
Insulators, 

Table of conductors and, 105. 

and conductors, 54, 104. 
Ions, 80. 

J. 

Joint resistance, 141. 
Joule, Definition of, 213. 
Joule's law for the heating of con- 
ductors, 268. 
equivalent, 217. 

K. 

Keepers, 38. 

Kilowatt, Definition of, 218. 

Kilowatt-hour, Definition of, 218. 



Lamps (See Arc and Incandescent) . 
Lenz's Law of induced currents, 

297. 
Local action in a battery, 61. 

M. 

Magnet, Artificial, 1. 

Axis of, 20. 

Breaking a, 24 

Compound and laminated, 10. 

Definition of, 2. 

Equator of, 20. 

Horseshoe, 10. 

Lifting power of, 27, 198. 

Making a permanent steel, 9. 

Natural, 1. 

Poles of, 2. 

Strength of, 26. 

To make an artificial, 6. 

Two poles of, inseparable, 4. 
Magnets, 

Classification of, 4. 
Magnetic 

action and reaction equal and 
opposite, 29. 

attraction and repulsion, 2. 

bodies free to move, 36, 203. 

circuit, Compound, 188. 

circuit of Manchester field 
frame, 373. 

circuits, 36, 187. 

declination, 43. 

dip needle, 12. 

effect of a current, 78. 

field, 16. 

field at the centre of a circular 
wire, 160. 

field of a circular wire, 160. 

field of an electromagnet, 186. 

field of a solenoid, 165. 

field of a straight current-car- 
rying wire, 153. 

field of the earth and its 
equator, 42. 

fields of parallel currents, 280. 

fields, Making, 16. 

force, 14. 

force, Two kinds of, 3. 

inclination or dip, 44. 

induction, 29. 

induction experiments, 28. 

induction, Tractive force and, 
198. # 

inductive effect of like and un- 
like poles, 31. 

leakage, 188. 

lines of force, 14. 

maps or charts, 44. 



INDEX. 



459 



Magnetic 

meridian, 43. 

needle, Deflection of, by a cur- 
rent, 157. 

needle, Horizontal, 11. 

polarity, Eeversed, 32. 

saturation, 24. 

screens, 32. 

substances, 4. 
Magnetisable metals, 4. 
Magnetisation by divided stroke, 7. 

by an electric current, 7. 

by an electromagnet, 8. 

curve, 197. 

of iron and steel by an electric 
current, 184. 
Magnetising force — Ampere-turns, 
192. 

force of a coil, To find, 193. 
Magnetism, Destruction of, by heat, 
26. 

Earth's, 41. 

earth's, Graphical representa- 
tion of, 42. 

Molecular theory of, 22. 

molecular theory, Experiment- 
al proof of, 23. 

Nature of, 22. 

Neutralizing the earth's, 47. 

Oscillation test for, 38. 

Residual, 196. 

Test for distribution of, 37. 
Magneto alternator, 342. 

dynamo, 375. 
Mass and weight, 210. 
Megohm, 106. 
Microhm, 106. 
Microphone principle, The, 327. 

transmitter, Blake, 328. 
Milliammeter, 200. 
Millivoltmeter, 207. 
Motor, 

Advantage of counter E. M. F. 
of, 400. 

and dynamo, Comparison be- 
tween, 393. 

and dynamo, Difference be- 
tween, 399. 

Automatic regulation of speed 
of, 401. 

brushes, Position of, 397. 

Counter E.M. F. of, 397. 

Direction of rotation of series 
and shunt, 395. 

Efficiency of, 410. 

Mechanical work performed by 
a, 402. 

Neutral point of, 397. 

Normal speed of a, 401. 

Operating a, 408. 



Motor, 

Output and rating of, 403. 

Principle of the, 394. 

regulation, Methods of, 405. 

Shunt, 396. 

Speed of, 402. 

speed and torque, 404. 

speed regulation, Methods of 
405. 

speed regulation, Series, 406. 

Starting a shunt, 410. 

starting box, 408. 

starting box, Automatic, 409. 

street car, Calculations for per- 
formance of, 411. 

Student's experimental, 396. 

test, 401. 

To find counter E. M. F. of, 
399. 

To find mechanical power de- 
veloped by, 399. 

To find the current through 
armature of, 398. 

torque, 402, 404. 

Tractive force of, 411. 

wiring calculations, 433. 
Motors, 

Classification of, 404. 

for railway work, Series, 407.. 
Multiple circuits (See Circuits). 
Multipliers, 148. 

N. 

Neutral point, 362. 

of a dynamo, To find, 365. 
Non-inductive winding, 150. 



Ohm, Definition of, 106. 
Ohm's Law, 119. 

applied to a battery circuit, 
122. 
Ohmmeter, Direct reading, 262. 



Parallax, Errors due to, 206. 
Parallel connections, Advantage 
of, 132. 

connection of batteries, 128. 
Permeability, 185. 
Pilot lamp, 378. 
Polarity indicator, 83. 

of a circular current, 161. 

of an iron ring, 188. 

of a solenoid. Testing the, 164. 

of a solenoid, Rules for deter- 
mining, 164. 

Reversed, 32. 



460 



INDEX. 



Polarization of a battery, 58. 

Remedies for, 63. 

test, 59. 
Pole, Negative, 54. 

pieces, armatures and keepers, 
38. 

Positive, 54. 
Poles, Consequent, 32, 188, 373. 

or electrodes and plates, 54. 
Potential difference and electromo- 
tive force, Measurement of, 
236. 

difference, Electromotive force 
and, 228, 241. 

difference, Variation of, with 
variation of external resis- 
tance, 235. 

in a circuit, Distribution of, 
233, 241. 
Potentiometer, Comparison of the 

E. M. F. of cells by, 243. 
Power, 210. 

calculations, Electrical, 215, 
219. 

Difference between energy, 
force, work and, 212. 

Electrical, 214. 

formulae, Electrical, 222. 

from cells, 223. 

transmission, 428. 

transmission, Efficiency of, 397. 

Units of electrical, 217. 

Unit of mechanical, 211. 
Pressure, current and resistance, 
Variation of, 235. 

Measurement of electrical, 228. 

R. 

Radiograph, 324. 

Railway calculations. Street, 411. 

motors, Connections for two, 
Plate I. 

work, Series motors for, 407. 
Reactance, Impedance and, 311. 
Reluctance, 193. 

Rheostat, Automatic motor start- 
ing, 409. 

Commercial, 148. 

Dynamo field, 381. 

Motor starting, 408. 
Rheostats, Laboratory, 150. 
Roentgen rays, 324. 
Roget's jumping spiral, 283. 
Resistance, Apparent, 311. 

Calculation of, 109, 121. 

Compensating, 148. 

external, Variation of, with 
potential difference, 235. 

Inductive, 311. 



Resistance, 
Joint, 141. 
Laws of, 107. 

of a battery, Internal, 116. . 
of commercial apparatus, 150. 
of solutions, Table of, 116. 
of metals, Table of, 115. 
of electrolytic conductors, 109. 
of human body, 151. 
of connections, 149. 
of wire, To calculate, 114. 
of metals, 109. 
of an armature, 348. 
of battery solutions, 109. 
of arc and incandescent lamps 

while burning, Measuring, 

248. 
of carbon, 109. 

of mil-foot of the metals, 110. 
Property-of, 103. 
Temperature and, 109. 
to temperature, Relation of, 

271. 
Unit of, 106. 
Resistance, Measurement of, 

by student's Wheatstone bridge, 

lozenge pattern, 257. 
by fall of potential, 247. 
by the substitution method, 

249. 
by the drop method of compar- 
ison, 250. 
by voltmeter method, 251. 
by Weston instruments, 252. 
by Wheatstone slide wire 

bridge, 252. 
Resistances, 

in parallel, Equal, 141. 

in parallel, Unequal, 142. 

in parallel, Conductivity 

method for calculating, 143. 
in multiple-series, 143. 
in series, Calculation of, 140. 
of commercial apparatus, 150. 
Residual Magnetism, 196. 

volts, 378. 
Resistivity defined, 103. 



S 



Self-Induction, 308. 

Neutralizing the effects of, 312. 
Series connection of batteries, 126. 
connection of batteries, Ad- 
vantage of, 133. 
Shunt, Weston ammeter, 206. 

To find the multiplying power 

of, 146. 
To find the value of, for a cer- 
tain multiplying power, 147. 



INDEX. 



461 



Shunted galvanometer, To find the 

current through, 147. 
Shunts, 145. 

Sines and tangents, Table of nat- 
ural, 173. 
Slide wire bridge, 254. 
Solenoid, Attractive force of, for 
an iron core, 186. 

Graphic field of a, 165. 

Helix and, 162. 
Spark coil, Gas lighting, 309. 

dimensions, 322. 

(See also Induction Coil). 
Sparking, 

Causes of, 367. 

distances in air, 321. 
Square mil defined, 111. 

area, Calculation of, 112. 
Storage Battery ( See Accumulator ) . 

T. 

Tangent galvanometer (See Gal- 
vanometer), 
of an angle, The, 172. 
Tangents, Table of natural sines 

and, 173. 
Telegraph apparatus, Resistance of 
151. 
key, 329. 
relay, 330. 

signal system and circuits, 330. 
sounder, 329. 
Telegraphy, Wireless, 331. 
Telephone, apparatus, Resistance 
of, 151. 
Bell, 326. 
Temperature coefficients, 272. 

Relation of resistance to, 271. 
Thermometer scales, Relation be- 
tween Farenheit and Centi- 
grade, 270. 
Three- Wire System, 431. 
Torque of a motor, 402. 
Traction, Electric, 411. 
Transformer, Step-up, 316. 

Principle of the induction coil 
or, 315. 
Transformers, Resistance of, 151. 

IT. 

Units of area, Equivalents of, 447. 

of energy and work, Equiva- 
lents of, 449. 

of heat, Equivalents of, 452. 

practical electrical, Definitions 
of, 445. 

of volume, Equivalents of, 447. 

of weight, Equivalents of, 448. 



V. 

Vacuum tubes, 323. 

Voltages, Measuring high, with a 

low range instrument, 240. 
Voltaic cell (See Battery). 
Voltameter calculations, 95. 

Copper, 95. 

Definition of, 80. 

gas, Construction of, 97. 

gas, Directions for using, 97. 

Measurements with a, 240. 

Weight, 95. 
Volta's Pile, 53. 

Voltmeter, Measuring high volt- 
ages with a low range, 240. 

method for measuring resist- 
ance, 251. 

Weston, 238. 
Voltmeters, Construction of, 238. 

Connecting, 239. 

Resistance of, 150. 
Volts lost, Hydraulic analogy to 
illustrate, 228. 

in an electric circuit, 230. 

in wiring leads, 242. 

on copper wire, Table of, 452. 



w. 

Watt, Definition of, 214. 
Watt-hour, Definition of, 218. 
Wattmeter, Dynamometer, 286. 
Thomson recording, 288. 
Weston direct reading, 287. 
Welding, Electric, 273. 
Wheatstone bridge, Best selection 
of arms for, 260. 
Commercial, 260. 
Lamp chart analogy of, 253. 
lozenge pattern, 257. 
Operating, 259. 
slide wire pattern, 252. 
To measure high and low re- 
sistance with, 260. 
Wire calculations, 114. 

gauge, B. & S., for copper wire, 

113. 
gauges, 112. 
gauges, Camparative table of, 

450. 
measure, The circular mil, 110. 
weight of, To calculate, 115. 
Wires, Calculation of circular mil 
area of, 111. 
fused by 100 amperes, Gauges, 
of, 273. 
Wiring, Arc lamp, 422. 

calculations, Incandescent, 429, 



462 



INDEX. 



Wiring, 

calculations, Motor, 433. 

Incandescent lamp, 426. 

leads, Volts lost in, 242. 

Loss on transmission lines in, 
428. 

Three- wire system of, 431. 

Two-wire multiple system of, 
426. 
Wireless telegraphy, 331. 
Work, 210. 



Work, 

Calculation of electrical, 213. 

Electrical, 212. 

Equivalents of mechanical and 

electrical, 216, 449. 
Heat and, 215. 
performed by a motor, 402. 
Unit of, 210. 



X. 



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LIST OF WORKS 



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THE IJ&f BOUND TIT "PLEASE 



JUNE. 66 

'^■p^ N. MANCHESTER, I 
INDIANA J 






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